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Chapter 4: Measurements and Significant Figures A significant figure is a digit that is a reliable indicator of value. Significant figure conventions guide us when we report the results of measurements so that what we report indicates the exactness of the measuring device.

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Chapter 4: Measurements and Significant Figures

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Chapter 4, Box 1 (p.53) 1.The number of significant figures is related to the certainty of a measurement or a count of great magnitude. (number of microscopes in lab vs. number of sand grains on beach)

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Chapter 4, Box 1 (p.53) 2. When reporting a measurement, record as many digits as are certain plus one digit that is estimated. (with meter or ruler, estimate last place…..on digital display, assume instrument estimated last place)

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Chapter 4, Box 1 (p.53) 3. All non-zero digits in a number are significant. (98.34 has four significant figures)

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Chapter 4, Box 1 (p.53) 4. All zeros between two non- zero digits are significant (100.4 has four significant figures)

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Chapter 4, Box 1 (p.53) 5. Zero digits to the right of a non-zero digit but to the left of an assumed decimal point may or may not be significant. $156,400,000 place holders, but not significant figures

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Chapter 4, Box 1 (p.53) 6. All zeros to the right of a decimal point and to the right of a non-zero digit before a decimal place are significant. 340.00 0.34000 3.4000 all have five significant figures

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Chapter 4, Box 1 (p.53) 7. All digits to the left of a non- zero digit and to the right of a decimal point are not significant unless there is a significant digit to their left. 0.0098 two significant figures 0.4098 four significant figures

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Chapter 4, Box 2 (p.55) 1. It is assumed that the last digit of a result from a calculation is rounded. 2. When rounding: a. If the digit to be dropped is less than 5, the preceding digit remains the same. Ex. 54.83 is rounded to 54.8

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Chapter 4, Box 2 (p.55) 2. When rounding: b. If the digit to be dropped is 5 or more, the preceding digit increases by one. Ex. 54.78 is rounded to 54.8 Ex. 54.65 is rounded to 54.7

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Chapter 4, Box 2 (p.55) 3. Round after performing a calculation. 4. Rule for addition or subtraction is different than for multiplication or division. Depends on number of places to the right of the decimal point

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Chapter 4, Box 2 (p.55) 4. Rule for addition or subtraction is different than for multiplication or division. Depends on number of places to the right of the decimal point (least) 98.0008 7.9878 +56.2 162.1886 round to 162.2

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Chapter 4, Box 2 (p.55) 5. In multiplication and division, keep as many significant figures as are found in the number with the least significant digits. 0.54678 X 0.980 X 7.899 = 3 significant figures 4.23

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Significant Digits The “Pacific-Atlantic” Rule for Significant Digits: If a decimal is Present, start counting from the Pacific side 0.00650 123 3 significant digits first non- zero digit

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Significant Digits The “Pacific-Atlantic” Rule for Significant Digits: If a decimal is Absent, start counting from the Atlantic side 12303000 123 5 significant digits first non- zero digit 45

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