L2.c-Calculations-of-Scientific-Notation.pdf
- 1. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION
- 2. Review: Scientific notation expresses a number in the form: M x 10n Any number between 1 and 10 n is an integer
- 3. 4 x 106 + 3 x 106 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 7 x 106 _______________
- 4. 4 x 106 + 3 x 105 If the exponents are NOT the same, we must move a decimal to make them the same.
- 5. Determine which of the numbers has the smaller exponent. 1. Change this number by moving the decimal place to the left and raising the exponent, until the exponents of both numbers agree. Note that this will take the lesser number out of standard form. 2. Add or subtract the coefficients as needed to get the new coefficient. 3. The exponent will be the exponent that both numbers share. 4. Put the number in standard form.
- 6. 4.00 x 106 + 3.00 x 105 + .30 x 106 Move the decimal on the smaller number to the left and raise the exponent ! 4.00 x 106 Note: This will take the lesser number out of standard form.
- 7. 4.00 x 106 + 3.00 x 105 + .30 x 106 4.30 x 106 Add or subtract the coefficients as needed to get the new coefficient. The exponent will be the exponent that both numbers share. 4.00 x 106
- 8. Make sure your final answer is in scientific notation. If it is not, convert it to scientific notation.!
- 9. A Problem for you… 2.37 x 10-6 + 3.48 x 10-4
- 10. 2.37 x 10-6 + 3.48 x 10-4 Solution… 002.37 x 10-6
- 11. + 3.48 x 10-4 Solution… 0.0237 x 10-4 3.5037 x 10-4
- 13. Rule for Multiplication When multiplying with scientific notation: 1.Multiply the coefficients together. 2.Add the exponents. 3.The base will remain 10.
- 14. (2 x 103) • (3 x 105) = 6 x 108
- 15. (4.6x108) (5.8x106) =26.68x1014 Notice: What is wrong with this example? Although the answer is correct, the number is not in scientific notation. To finish the problem, move the decimal one space left and increase the exponent by one. 26.68x1014 = 2.668x1015
- 16. ((9.2 x 105) x (2.3 x 107) = 21.16 x 1012 = 2.116 x 1013
- 17. (3.2 x 10-5) x (1.5 x 10-3) = 4.8 • 10-8
- 18. Rule for Division When dividing with scientific notation 1.Divide the coefficients 2.Subtract the exponents. 3.The base will remain 10.
- 19. (8 • 106) ÷ (2 • 103) = 4 x 103
- 20. Please multiply the following numbers. (5.76 x 102) x (4.55 x 10-4) = (3 x 105) x (7 x 104) = (5.63 x 108) x (2 x 100) = (4.55 x 10-14) x (3.77 x 1011) = (8.2 x10-6) x (9.4 x 10-3) =
- 21. 1. (5.76 x 102) / (4.55 x 10-4) = 2. (3 x 105) / (7 x 104) = 3. (5.63 x 108) / (2) = 4. (8.2 x 10-6) / (9.4 x 10-3) = 5. (4.55 x 10-14) / (3.77 x 1011) = Please divide the following numbers.
- 22. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION Raising Numbers in Scientific Notation To A Power
- 23. (5 X 104)2 = (5 X 104) X (5 X 104) = (5 X 5) X (104 X 104) = (25) X 108 = 2.5 X 109
- 24. 1. (3.45 X 1010)2 2. (4 X 10-5)2 3. (9.81 X 1021)2 Try These: 1. (3.45 X 1010)2 = (3.45 X 3.45) X (1010 X 1010) = (11.9) X (1020) = 1.19 X 1021 2. (4 X 10-5)2 = (4 X 4) X (10-5 X 10-5) = (16) X (10-10) = 1.6 X 10-9 3. (9.81 X 1021)2 = (9.81 X 9.81) X (1021 X 1021) = (96.24) X (1042) = 9.624 X 1043 1.19 X 1021 1.6 X 10-9 9.624 X 1043
- 25. Changing from Standard Notation to Scientific Notation Ex. 6800 6800 1. Move decimal to get a single digit # and count places moved 2. Answer is a single digit number times the power of ten of places moved. 68 x 10 3 If the decimal is moved left the power is positive. If the decimal is moved right the power is negative. 1 2 3 What is Scientific Notation A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10 (eg, 7000 = 7 x 103 or 0.0000019 = 1.9 x 10 -6) It’s a shorthand way of writing very large or very small numbers used in science and math and anywhere we have to work with very large or very small numbers. Why do we use it? Changing from Scientific Notation to Standard Notation Ex. 4.5 x 10-3 1. Move decimal the same number of places as the exponent of 10. (Right if Pos. Left if Neg.) 00045 1 2 3 Multiply two numbers in Scientific Notation (3 x 104)(7 x 10–5) 1. Put #’s in ( )’s Put base 10’s in ( )’s 2. Multiply numbers 3. Add exponents of 10. 4. Move decimal to put Answer in Scientific Notation = (3 x 7)(104 x 10–5) = 21 x 10-1 = 2.1 x 100 or 2.1 6.20 x 10–5 8.0 x 103 DIVIDE USING SCIENTIFIC NOTATION = 0.775 x 10-8 = 7.75 x 10–9 1. Divide the #’s & Divide the powers of ten (subtract the exponents) 2. Put Answer in Scientific Notation 6.20 8.0 10-5 103 9.54x107 miles 1.86x107 miles per second Addition and subtraction Scientific Notation 1. Make exponents of 10 the same 2. Add 0.2 + 3 and keep the 103 intact The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same. 2.0 x 102 + 3.0 x 103 .2 x 103 + 3.0 x 103 = .2+3 x 103 = 3.2 x 103 2.0 x 107 - 6.3 x 105 2.0 x 107 -.063 x 107 = 2.0-.063 x 107 = 1.937 x 107 1. Make exponents of 10 the same 2. Subtract 2.0 - .063 and keep the 107 intact Scientific Notation Makes These Numbers Easy