Chapter 4: Measurements and Significant Figures

1. 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.

2. Chapter 4: Measurements and Significant Figures

3. Chapter 4, Box 1 (p.53) • 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)

4. 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)

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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. Significant Digits The “Pacific-Atlantic” Rule for Significant Digits: If a decimal is Present, start counting from the Pacific side first non-zero digit 1 2 3 3 significant digits 0.00650

16. Significant Digits The “Pacific-Atlantic” Rule for Significant Digits: If a decimal is Absent, start counting from the Atlantic side first non-zero digit 5 significant digits 5 4 3 2 1 12303000