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The document discusses the rules for entering mathematical expressions into calculators, apps, and software using the BASIC input format. It explains that expressions from books cannot be directly typed in, and covers the syntax and semantics of the BASIC format. The format uses symbols like +, -, *, /, and ^ for operations and follows the order of operations like PEMDAS. The document provides examples of syntax errors and discusses how semantics are the rules for interpreting the meaning of syntactically correct expressions.

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Calculator Input
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software.
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC.
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.)
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”,
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8),
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”,
Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”, and the power operation is “ ^ ” (or shift + 6).
Calculator Input 2 5 Mathematics expressions such 8 or3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”, and the power operation is “ ^ ” (or shift + 6). So the BASIC–input for 32 is “3^2” and for 4 x 32, it’s “4*3^2”.
Calculator Input 2 5 Mathematics expressions such 8 or3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”, and the power operation is “ ^ ” (or shift + 6). So the BASIC–input for 32 is “3^2” and for 4 x 32, it’s “4*3^2”. Finally, we also use “+" and “–” as signs however this may or may not be the case depending on the calculator or software.
Power Equations and Calculator Input Syntax
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input.
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?).
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”.
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” for the subtraction operation
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors.
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors. * It take two quantities to perform +, --, *, / and ^.
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors. * It take two quantities to perform +, --, *, / and ^. Inputs such as “6*”, “23 /”, or “7^” generate error–messages.
Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors. * It take two quantities to perform +, --, *, / and ^. Inputs such as “6*”, “23/”, or “7^” generate error–messages. Note that “+6” is OK but “6+” generates an error.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions. The semantics for BASIC– format inputs are the same as the rules for order of operations PEMDAS.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions. The semantics for BASIC– format inputs are the same as the rules for order of operations PEMDAS. A semantic input mistake is a mistake where we mean to execute one set of calculations without realizing that the input is interpreted differently by the machine.
Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions. The semantics for BASIC– format inputs are the same as the rules for order of operations PEMDAS. A semantic input mistake is a mistake where we mean to execute one set of calculations without realizing that the input is interpreted differently by the machine. Here are some examples of similar but different inputs.
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2 The correct BASIC format is “(–2–4^(1/2))/2”.
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2 The correct BASIC format is “(–2–4^(1/2))/2”. The answer is 0.
Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2 The correct BASIC format is “(–2–4^(1/2))/2”. The answer is 0. When in doubt, insert ( )’s to specify the order of operations.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123.
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3 x = (8/3) 3/2
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3 x = (8/3) 3/2 The exact answer
Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3 x = (8/3) 3/2 The exact answer ≈ 4.35 The approx. answer
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 We swapped sides to avoid negative signs.
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3 0.2x + 1.3 = (5.9/3.3)3
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3 0.2x + 1.3 = (5.9/3.3)3 0.2x = (5.9/3.3)3 – 1.3
Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3 0.2x + 1.3 = (5.9/3.3)3 0.2x = (5.9/3.3)3 – 1.3 (5.9/3.3)3 – 1.3 x= ≈ 22.1 0.2
Power Equations and Calculator Input Exercise A. Find the syntax error in each of the following expressions. 1. 4*–3 2. 4*(–3] 3. 2(4–(3(5)) 4. 7–(3)/*5 5. 2^(–3)+(1^2(/6)) 6. 2^(–3)(1^2+/(6)) Exercise B. Translate each of the following book expressions into the BASIC–format. Do not calculate. 5 4 +3 4 4+3 8. 4+3 9. 5 10. 5(6) 7. 5 3+4 6 11. 5(6) 12. 3(4+5) 13. 5+2 + 1 14. 7 + 6–3 5(6–7) 5–8 5 –1 6 +1 15. 5+3 16. 5+2 6 –2 7 + 6–3 5 5(8)
Power Equations and Calculator Input Exercise C. Translate each of the following BASIC–expression into the book–format. Calculate the answer by hand and confirm it with a calculator. 17. 4*2–3/2 – 5 18. 4*2–3/2–(5) 19. 4*(2–3/2)–5 20. 4*2–3/(2–5) 21. 4*(2–3)/2–5 22. 4*(2–3/2–5) Exercise D. Translate each of the following BASIC–expression into the book–format. Calculate part a. by hand and the part b by a calculator. 23. a. 4/2*3 b. 1.234/3.24*0.11 24. a. 3+8/(–2*2) b. 3.73–4.83/(3.54–2.12) 25. a. –2^2+6/3 b. –2.212+6.33/0.64 26. a. (–2)^2+6/3 b. (–2.21)2–6.33/3.64 27. a. (–2)^2*2/(–2)^2(–2) b. (–2.84)3*2/4.43–3 28. a. (–2^2)*2/(–2)^2(2)4 b. –3.432 /3.413*0.83 29. a. 4(–2)^2–2/(–2)^–3*2 b. 4.05*22–6.32/3.413–6 30. a. (–2)^((2*2)/–2)^2*2 b. 16.7/2.102–4.933/1.04

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12 calculator input

  • 2. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software.
  • 3. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC.
  • 4. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.)
  • 5. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”,
  • 6. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8),
  • 7. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”,
  • 8. Calculator Input 2 5 Mathematics expressions such 8 or 3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”, and the power operation is “ ^ ” (or shift + 6).
  • 9. Calculator Input 2 5 Mathematics expressions such 8 or3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”, and the power operation is “ ^ ” (or shift + 6). So the BASIC–input for 32 is “3^2” and for 4 x 32, it’s “4*3^2”.
  • 10. Calculator Input 2 5 Mathematics expressions such 8 or3 3 + x2 that appeared in books can’t be keyboarded directly “as is” into calculators, smart phone apps or computer software. While there is no standard input method that would work for all of them, most keyboard mathematics–input methods are similar to the BASIC–input method which is used in the computer language BASIC. For example, the book–format 3 is “3/4” in the 4 BASIC format. (All calculator–inputs through out this course will be in “quoted boldface”.) In the BASIC–format, addition and subtraction are “+” and “–”, multiplication operation is “ * ” (or shift + 8), the division operation is “ / ”, and the power operation is “ ^ ” (or shift + 6). So the BASIC–input for 32 is “3^2” and for 4 x 32, it’s “4*3^2”. Finally, we also use “+" and “–” as signs however this may or may not be the case depending on the calculator or software.
  • 11. Power Equations and Calculator Input Syntax
  • 12. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input.
  • 13. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?).
  • 14. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”.
  • 15. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
  • 16. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3
  • 17. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” for the subtraction operation
  • 18. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation
  • 19. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors.
  • 20. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors. * It take two quantities to perform +, --, *, / and ^.
  • 21. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors. * It take two quantities to perform +, --, *, / and ^. Inputs such as “6*”, “23 /”, or “7^” generate error–messages.
  • 22. Power Equations and Calculator Input Syntax The word “syntax” refers to the rules for recognizable input. If we enter “5 + ” in the calculator, press “enter”, we get an error message (5 plus what?). Such an error where the input is incomplete or gibberish is called a “syntax error”. Example A. Find the syntax error in each of the following expressions. a. (6+(3–)) b. (6–4(0–(–1)) c. 1.3*2.1/(4.3*)^3 Missing a quantity Missing a “ ) ” Missing a quantity for the subtraction for the multiplication operation operation Following are some of the common syntax errors. * It take two quantities to perform +, --, *, / and ^. Inputs such as “6*”, “23/”, or “7^” generate error–messages. Note that “+6” is OK but “6+” generates an error.
  • 23. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it.
  • 24. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs.
  • 25. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings.
  • 26. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message.
  • 27. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “.
  • 28. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics
  • 29. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions.
  • 30. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions. The semantics for BASIC– format inputs are the same as the rules for order of operations PEMDAS.
  • 31. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions. The semantics for BASIC– format inputs are the same as the rules for order of operations PEMDAS. A semantic input mistake is a mistake where we mean to execute one set of calculations without realizing that the input is interpreted differently by the machine.
  • 32. Power Equations and Calculator Input * For every left parentheses “( ” opened , there must be a right parentheses “)” that closes it. Hence the number of “( ” should be the same the number of “)” in the inputs. * Symbols such as [ ] or { } may have different meanings. The machine always tell us when we made a syntax error with an error message. However another type of mistake that occurs often for which there is no warning and is difficult to catch are the “miscommunications “. Semantics Semantics are the rules for interpreting the "meaning“ of syntactically correct expressions. The semantics for BASIC– format inputs are the same as the rules for order of operations PEMDAS. A semantic input mistake is a mistake where we mean to execute one set of calculations without realizing that the input is interpreted differently by the machine. Here are some examples of similar but different inputs.
  • 33. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
  • 34. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
  • 35. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
  • 36. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. d. Write the BASIC input of 2–√4 . Find the answer. 2
  • 37. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2
  • 38. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2 The correct BASIC format is “(–2–4^(1/2))/2”.
  • 39. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2 The correct BASIC format is “(–2–4^(1/2))/2”. The answer is 0.
  • 40. Power Equations and Calculator Input Example B. a. Find “–8^2/3” with and without the calculator . –43 = –64 . The input yields –64/3 = –21.33… It’s 3 3 2 b. Write –8 in the BASIC input, find the answer with and 3 without the calculator. 2 The BASIC input of –8 is “–8^(2/3)”. The answer is –4. 3 c. Find “–2–4^(1/2)/2” with and without the calculator. The input yields –3 because it’s –2 –√4 . 2 d. Write the BASIC input of 2–√4 . Find the answer. 2 The correct BASIC format is “(–2–4^(1/2))/2”. The answer is 0. When in doubt, insert ( )’s to specify the order of operations.
  • 41. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations.
  • 42. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application.
  • 43. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point.
  • 44. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits.
  • 45. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit.
  • 46. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4
  • 47. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123.
  • 48. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1
  • 49. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8
  • 50. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3
  • 51. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3 x = (8/3) 3/2
  • 52. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3 x = (8/3) 3/2 The exact answer
  • 53. Power Equations and Calculator Input We use calculators to obtain approximate decimal answers for irrational solutions of power equations. The accuracy of the approximation required depends on the application. For example, if the problem is about money, then we round off at to the penny, i.e. the 2nd position after the decimal point. However all other decimal answers in this course are rounded off to three significant digits. To obtain this, start from the 1st nonzero digit, count and round off at the third digit. For example, 12.35 ≈ 12.4 0.001234 ≈ 0.00123. Example C. Solve for x and find the approximate solution. a. 3x2/3 – 7 = 1 3x2/3 = 8 x2/3 = 8/3 x = (8/3) 3/2 The exact answer ≈ 4.35 The approx. answer
  • 54. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3
  • 55. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3
  • 56. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 We swapped sides to avoid negative signs.
  • 57. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9
  • 58. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3
  • 59. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3 0.2x + 1.3 = (5.9/3.3)3
  • 60. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3 0.2x + 1.3 = (5.9/3.3)3 0.2x = (5.9/3.3)3 – 1.3
  • 61. Power Equations and Calculator Input b. 1.3 = 7.2 – 3.3(0.2x + 1.3)1/3 3.3(0.2x + 1.3)1/3 = 7.2 – 1.3 3.3(0.2x + 1.3)1/3 = 5.9 (0.2x + 1.3)1/3 = 5.9/3.3 0.2x + 1.3 = (5.9/3.3)3 0.2x = (5.9/3.3)3 – 1.3 (5.9/3.3)3 – 1.3 x= ≈ 22.1 0.2
  • 62. Power Equations and Calculator Input Exercise A. Find the syntax error in each of the following expressions. 1. 4*–3 2. 4*(–3] 3. 2(4–(3(5)) 4. 7–(3)/*5 5. 2^(–3)+(1^2(/6)) 6. 2^(–3)(1^2+/(6)) Exercise B. Translate each of the following book expressions into the BASIC–format. Do not calculate. 5 4 +3 4 4+3 8. 4+3 9. 5 10. 5(6) 7. 5 3+4 6 11. 5(6) 12. 3(4+5) 13. 5+2 + 1 14. 7 + 6–3 5(6–7) 5–8 5 –1 6 +1 15. 5+3 16. 5+2 6 –2 7 + 6–3 5 5(8)
  • 63. Power Equations and Calculator Input Exercise C. Translate each of the following BASIC–expression into the book–format. Calculate the answer by hand and confirm it with a calculator. 17. 4*2–3/2 – 5 18. 4*2–3/2–(5) 19. 4*(2–3/2)–5 20. 4*2–3/(2–5) 21. 4*(2–3)/2–5 22. 4*(2–3/2–5) Exercise D. Translate each of the following BASIC–expression into the book–format. Calculate part a. by hand and the part b by a calculator. 23. a. 4/2*3 b. 1.234/3.24*0.11 24. a. 3+8/(–2*2) b. 3.73–4.83/(3.54–2.12) 25. a. –2^2+6/3 b. –2.212+6.33/0.64 26. a. (–2)^2+6/3 b. (–2.21)2–6.33/3.64 27. a. (–2)^2*2/(–2)^2(–2) b. (–2.84)3*2/4.43–3 28. a. (–2^2)*2/(–2)^2(2)4 b. –3.432 /3.413*0.83 29. a. 4(–2)^2–2/(–2)^–3*2 b. 4.05*22–6.32/3.413–6 30. a. (–2)^((2*2)/–2)^2*2 b. 16.7/2.102–4.933/1.04