Which of these measurements do you consider to be most precise? 21.5 inches 21.501 inches

1. Which of these measurements do you consider to be most precise? • 21.5 inches • 21.501 inches • 21.50 inches • 21 inches

2. Scientific Measurement Chapter 3

3. Significant Figures • A. Which figures “count” in a calculated answer? • B. The rules are different for “multiplication and division” than for “addition and subtraction”

4. C. These are the textbook rules to determine which figures are significant: (these apply to multiplication and division problems)

5. Every nonzero digit in a measurement is considered significant • 2. Zeroes between nonzero digits are significant • Leftmost zeroes appearing in front of nonzero digits are NOT significant • Zeroes at the end of numbers and to the right of a decimal point are always significant

6. 5. Zeroes at the rightmost end of a number that lie to the left of an understood decimal are NOT significant 6. Quantities that have been counted have unlimited significant figures

7. D. Simplified significant digit rules: • Numbers with decimal points: • a) Zeroes in the front of any • number DON’T count • b) Once you start counting, don’t • stop • 2) Numbers without decimal points: • - Every digit counts except ending zeroes

8. 1) Numbers with decimal points: a) Zeroes in the front of any number DON’T count b) Once you start counting, don’t stop 2) Numbers without decimal points: - Every digit counts except ending zeroes • Ex: How many sig figs in these numbers: • 0.00251 • 1.0025 • 2300 • 0.10000 • 23.10

9. 1) Numbers with decimal points: a) Zeroes in the front of any number DON’T count b) Once you start counting, don’t stop 2) Numbers without decimal points: - Every digit counts except ending zeroes • How many sig figs in these numbers: • 2105.0 • 0.00500 • 0.008 • 57.200 • 59,810

10. II. Multiplication and Division A. Calculated answers cannot have more sig figs than the number used with the fewest Ex: 3.22 x .15 3 sig figs 2 sig figs 0.483 = 0.48

11. 0.0025 x 2.12 0.0053

12. 0.0025 x 0.0101 0.000025

13. 1250 x 0.110 138

14. 10.0 2.0 = 5.0

15. III. Scientific Notation A. Very large and very small numbers are more conveniently written in scientific notation: Ex: 2,785,000 = 2.785 x 106 0.0000125 = 1.25 x 10-5

16. Ex: Convert these numbers into scientific notation: = 9.452 x 104 94,520 = 2.000 x 10-3 0.002000 Ex: Convert these numbers into regular numbers: = 0.0125 1.25 x 10-2 = 350,000 3.50 x 105

17. 6.52 x 109 X 5.2 x 104 3.4 x 1014

18. 2.10 x 10-3 9.9 x 10-4 = 2.1

19. III. Rules for Addition and Subtraction A. The number of decimal places in a calculated answer is limited by the number used with the fewest Ex: 3.221 + .15 3.371 = 3.37

20. 0.0025 + 2.12 2.12

21. 25.19 - 24.9 0.3

22. 6.45 x 105 - 6.45 x 102 6.44 x 105

23. IV. The Metric System A. Specific units are assigned for various scientific measurements: 1) length = meter 2) volume = liter 3) mass = gram B. Fractions and multiples of these units use a prefix to indicate the amount

24. C. These prefixes are written before the liter, meter, gram words: Kilo hecta deka meter liter gram deci centi milli 1000 100 10 0.1 0.01 0.001 Examples using abbreviations: ml = milliliter centimeter cm = kilogram kg = m = meter