Significant Figures

1. Significant Figures

2. Why do we need to know significant figures? • We as scientists need to measure things as we perform experiments. • Instruments have different degrees of precision • We measure to the last known calibration, and estimate the unknown.

3. Significant = replaceable • A number is significant because it can be replaced by another number in a measurement

4. The Rules

5. Significant Figures – The Rules • 1. Nonzero numbers 1 – 9 are always significant. • Examples: • 1 meter 1 sig fig • 92liters 2 sig figs • 34578grams 5 sig figs

6. Significant Figures – The Rules • 2. Imbedded zeros (zeros between nonzero numbers) are always significant. • Examples: • 202cm 3 sig figs • 10509mL5 sig figs • 2039kg 4 sig figs • 90009g 5 sig figs

7. Significant Figures – The Rules • 3. Leading zeros are never significant. • 4. Trailing zeros after a nonzero number after the decimal are significant. • Examples: • 0.00000540 g 3 sig figs • 0.3700 mm 4 sig figs • 0.00101 L 3 sig figs

8. Significant Figures – The Rules • 5. Trailing zeros before the decimal are significant only if the decimal point is specified. • Examples: • 100. dg 3 sig figs • 100 dg 1 sig fig • 8900 km 2 sig figs • 8900. km 4 sig figs

9. Exact Numbers • An exact number is a number that cannot be changed. (Cannot be halved or split up) • Ex. 2 atoms, 1 proton, a hundred dollar bill • We include most conversion factors as exact numbers • Ex. 1m = 100 cm • When you work with exact numbers, you consider them to have infinite sig figs. (You don’t have to worry about them!)

10. RECAP #1 Leading Zeros Imbedded Zero 0.00770800 Nonzero numbersTrailing Zeros after the decimal

11. 6 significant figures

12. RECAP #2 Leading Zeros Imbedded Zero (none) 22060 Nonzero numbersTrailing zero with no decimal

13. 4 significant figures

14. Lets Practice!

15. 56 meters • 2 sig figs • Rule 1

16. 20 grams 1 sig fig Rule 1, 5

17. 303.0 mL 4 sig figs Rule 1, 2, 4

18. 200 dollars 1 sig fig Rule 1, 5

19. 207 donkeys 3 sig figs Rule 1,2

20. 0.7900 grams 4 sig figs Rule 1,3,4

21. 0.0096070 m 5 sig figs Rule 1,2,3,4

22. 102000 km 3 sig figs Rule 1,2,5

23. 1.10 x 102 hm 3 sig figs Rule 1, 4

24. 2.2 x 1034 atoms 2 sig figs Rule 1

25. Rounding Numbers • If you have to round and the number you are looking to round is less than 5, don’t round. • Example: 214 round to 2 s.f. Answer = 210

26. Rounding Numbers • If you have to round and the number you are looking to round is 5 or greater, round up. • Example: 215 round to 2 s.f. Answer = 220