Significant Figures

1. 3 1 2 Significant Figures

2. I. Significant Figures in Measurement • Includes all the digits that are known, plus one that is estimated

3. A. Measuring with a ruler

4. Practice What is the following measurement with the proper number of sig. figs.?

5. b. Measuring a Liquid **Measure from the bottom of the meniscus

6. Practice 1. 2.

7. 3. 4.

8. ii. Significant Figure Rules • Every nonzero number (1-9) is considered to be significant • 2,396 has four significant figures • “Oreo cookie rule” • Zeros between nonzero digits are significant • 50,006 has five significant figures • 101 has three significant figures

9. “After After rule” • Zeros after a non zero digit and after a decimal point are significant • 23.000 has five significant figures • 0.0456000 has sixsignificant figures

10. NO YES NO YES

11. How many significant figures are in the numbers below? 23,459 300,004 0.042 35.00000 670000 5 sig figs 6 sig figs 2 sig figs 7 sig figs 2 sig figs Question Time

12. Rounding Significant Figures • Determine how many significant figures are needed • Find the counting number— first nonzero number (starting from the left) • Count how many sig. figs. you need • Underline the last digit counted

13. Round the underlined digit by: • If the digit to the right of the underlined digit is less than five, the underlined digit stays the same and everything else becomes a zero place holder or gets dropped off • If the digit to the right of the underlined digit is more than five, the underlined digit is increased by one and everything else becomes zero place holder or gets dropped off **Five or more add one next door

14. Question Time Round each number to the specified number of sig. figs. • 3.454 (3 sig. fig.) goes to • 125,000 (2 sig. fig.) goes to • 7,905 (1 sig. fig.) goes to • 0.00369847 (2 sig. fig.) goes to • 629.55 (3 sig. fig.) goes to 3.45 130,000 8,000 0.0037 630 ( you can’t get three sig. fig. unless using Scientific Notation)

15. Significant figures in scientific notation • All digits in the coefficient are significant • The power of ten is not significant • 2.80 ×106 has 3 significant figures

16. Question Time Give the correct number of significant figures 2.3445 (5) 2.69 (3) 3.4 (2) • 2.3445 x 10-6 • 2.69 x 10 • 3.4 x 103

17. Question Time • Round each number to 3 significant figures • 87.073 meters • 4.3621 x 108 • 0.01552 meter • 9009 meters • 1.77777 x 10-3 87.1 meters 4.36 x 108 0.0155 meters 9010 meters 1.78 x 10-3

18. 3 1 2 Significant Figures with calculations

19. Multiplication and Division • Round the answer to the same number of significant figures as the measurement with the least number of significant figures • 7.55 × 0.34 = 2.567 3 sig. fig.2 sig. fig. • Answer ≈2.6 (2 sig. figs.)

20. 2.105 × 0.762 = 1.60401 4 sig fig. 3 sig. fig. Answer is 1.60 (3 sig. fig.) • 2.4526 ⁄ 8.4 =0.2919761 5 sig. fig 2 sig. fig Answer is 0.29 (2 sig. fig.)

21. Question Time Calculate using the appropriate number of sig. fig. 1300 (1310.4) 7 (7.28) 1.5 (1.5275) 0.4 (0.416667) 49.0 (49) • 23.4 x 56 • 1.456 x 5 • 0.065 x 23.5 • 25/60 • 245.00 / 5.00

22. Addition and Subtraction with Sig. Fig. • Your answer must have the same number of digits to the right of the decimal point as the value withthe fewest digits to the right of the decimal point • 28.0 + 23.538 + 25.68 = 77.218 (1) (3) (2) With correct sig fig. 77.2  (1 place)

23. Question Time Add or subtract using the correct number of significant figures 72 (72.045) 8 (7.9) 81.3 (81.303) 11.4 (11.3654) • 23.445 + 14 +34.6 • 26.9 – 19 • 34.543 + 12.56 + 34.2 • 45.5654 – 34.2