Chapter 4 Measurements and Significant Figures A significant

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 we report indicates the exactness of the measuring device.

Chapter 4: Measurements and Significant Figures

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)

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)

Chapter 4, Box 1 (p. 53) 3. All non-zero digits in a number are significant. (98. 34 has four significant figures)

Chapter 4, Box 1 (p. 53) 4. All zeros between two non-zero digits are significant (100. 4 has four significant figures)

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

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

Chapter 4, Box 1 (p. 53) 7. All digits to the left of a nonzero digit and to the right of a decimal point are not significant unless there is a significant digit to their left. 0. 0098 0. 4098 two significant figures four significant figures

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

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

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

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

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 = 4. 23 3 significant figures

Significant Digits The “Pacific-Atlantic” Rule for Significant Digits: If a decimal is Present, start counting from the Pacific side first nonzero digit 1 2 3 0. 00650 3 significant digits

Significant Digits The “Pacific-Atlantic” Rule for Significant Digits: If a decimal is Absent, start counting from the Atlantic side 5 significant digits 5 4 32 1 12303000 first nonzero digit