Chapter 2- Learning Outcome 2_Mathematics for Technologists
- 1. 21st Century Mathematics for the Industrial Technology Learners: Automotive Technology BABY 'RLENE I. BAYOC
- 2. Measurements and Scientific Notation Chapter II 21st Century Mathematics for the Industrial Technology Learners: Automotive Technology
- 3. CHAPTER II: Measurements and Scientific Notations Learning Outcome 2: Applied the rules of measurements and scientific notation in solving problems.
- 4. Significant figure is the digits in a measurement which is read and estimated on a scale. SIGNIFICANT FIGURES CHAPTER II: Measurements and Scientific Notations
- 5. A. To determine the number of significant figures in a number, use the following rules: 1. All non-zero numbers ARE significant. The number 38.7 has three significant figures because all of the digits present are non-zero. 2. Zeros between two non-zero digits are significant. 8001 has FOUR significant figures. The zeros are between nonzero digits 8 and 1. 3. Leading zeros are not significant. They are "place holders." The number 0.74 has only two significant figures. 0.0012 also has two significant figures. 4. Trailing zeros to the right of the decimal are significant. There are four significant figures in 97.00. 5. Trailing zeros in a whole are not significant. Writing just "3400" indicates that the zeros are not significant, and there are only two significant figures in this value. 6. Trailing zeros in a whole number with a bar placed on top of a zero are significant. "340 ." indicates that the trailing 0̅ zeros are significant; there are four significant figures in this value. 7. Exact numbers have an infinite number of significant figures. This rule applies to numbers that are definitions. For example, 1 meter = 1.00 meters = 1.0000 meters = 1.0000000000000000000 meters, etc. RULES FOR SIGNIFICANT FIGURES CHAPTER II: Measurements and Scientific Notations
- 6. RULES FOR SIGNIFICANT FIGURES B. Rounding off significant figures: To round off numbers, we simply drop all unwanted digits to the right of the digits that are to be retained and increase the last retained digit by 1 if the first dropped digit is 5 or greater. It may be necessary to replace dropped digits by zeros in order to hold the decimal point; for instance, we round off 8351.35 to the nearest hundred as 8400, to the nearest thousands as 8000, and to the nearest tenths as 8351.4. CHAPTER II: Measurements and Scientific Notations
- 7. C. For addition and Subtraction with significant figure: They should be rounded off to the precision of the least precise measurement. For example, add or subtract 321.36 and 51.2. First, we round off 321.36 to nearest tenth,this will give 321.4. Addition gives us 321.4 + 51.2 = 372.6. Subtraction gives us 321.4 - 51.2 = 270.2. RULES FOR SIGNIFICANT FIGURES CHAPTER II: Measurements and Scientific Notations
- 8. D. For multiplication and division with significant figure: The number of significant figures in the result is no greater than the number of significant figures in the measurement with the fewest significant figures. For example, multiply 12.3 by 2.5, longhand multiplication will give 30.75. The answer should be rounded off to 31 because 2.5 has two significant figures. The division will give 4.9 rounded from 4.92. RULES FOR SIGNIFICANT FIGURES CHAPTER II: Measurements and Scientific Notations
- 9. A. Addition and Subtraction of two numbers expressed in scientific notation. Before adding or subtracting two numbers expressed in scientific notation, their powers of ten must be equal or convert the numbers to ordinary decimal form then add or subtract. Convert the answer in scientific notation. For example, add or subtract 9.87x10^4 and 1.37x10^3, convert one of the two numbers to make their power of 10 equal. 1.37x10^3 = 0.137x10^4. Adding gives 10.007x10^4 = 1.0007x10^5. Subtracting gives 9.733x10^4. . OPERATIONS WITH SCIENTIFIC NOTATION CHAPTER II: Measurements and Scientific Notations
- 10. B. Multiplication of two numbers expressed in scientific notation. To multiply two numbers expressed in scientific notation, multiply separately their decimal parts and their powers of ten, then add their exponents. Express final answer in scientific notation. For example, (1.25x10^4)(4.98x10^7)= (1.25)(4.98)x10^(4+7) = 6.225x10^11 or 6.23x10^11 OPERATIONS WITH SCIENTIFIC NOTATION CHAPTER II: Measurements and Scientific Notations
- 11. C. Division of two numbers expressed in scientific notation. To divide two numbers expressed in scientific notation, divide separately their decimal parts and their powers of ten, then subtract their exponents. Express final answerin scientific notation. For example, (5.98x10^7)÷(2.7x10^4) = (5.98)÷(2.7)x10^(7-4) = 2.21481481x103 = 2.2x103 OPERATIONS WITH SCIENTIFIC NOTATION CHAPTER II: Measurements and Scientific Notations
- 13. CHAPTER II: Measurements and Scientific Notations Thank you