Significant Figures

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.

The Rules

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

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

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

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

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!)

0.00770800 RECAP #1 Leading Zeros Imbedded Zero after the decimal Nonzero numbers Trailing Zeros after the decimal

6 significant figures

22060 RECAP #2 (none) Nonzero numbers Trailing zero with no decimal Leading Zeros Imbedded Zero (none) 22060 Nonzero numbers Trailing zero with no decimal

4 significant figures

Lets Practice!

56 meters 2 sig figs Rule 1

20 grams 1 sig fig Rule 1, 5

303.0 mL 4 sig figs Rule 1, 2, 4

200 kilograms 1 sig fig Rule 1, 5

207 kilometers 3 sig figs Rule 1,2

0.7900 grams 4 sig figs Rule 1,3,4

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

102000 km 3 sig figs Rule 1,2,5

1.10 x 102 hm 3 sig figs Rule 1, 4

2.2 x 1034 atoms infinite sig figs

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

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

Adding and subtracting with significant figures. When adding or subtracting significant figures, you round your answer to the least number of places after the decimal that are contained in your problem.

YOU ARE LOOKING AT PLACES AFTER THE DECIMAL NOT SIGNIFICANT FIGURES!

Example: 2.00 + 4.0 = 6.0 You look for the least number of PLACES after the decimal. 2.00 = 2 places after the decimal 4.0 = 1 place after the decimal Your answer can only have one place after the decimal.

2.0 + 4 = 6 Example: 2.0 = 1 place after the decimal 4 = no places after the decimal Your answer can not have any places after the decimal.

Example: 0.05560 – 0.001 = 0.0546 =0.055 0.05560 = 5 places after the decimal 0.001 = 3 places after the decimal Your answer can only have 3 places after the decimal.

Let’s Practice 17.0 – 0.4753 = 16.5247 Answer 16.5

37.00 + 0.4753 + 19 = 56.4753 Answer 56

100.0 – 71.52 = 28.48 Answer 28.5

0.075 + 11 + 9.2 = 20.275 Answer 20

Multiplying and Dividing with Significant Figures When multiplying or dividing with significant figures, your answer must be rounded to the least number of significant figures in the problem.

YOU ARE LOOKING AT SIGNIFICANT FIGURES NOT PLACES AFTER THE DECIMAL!

Example 20.0 x 14.22 = 284.4 Answer 284

430 x 0.003 = 1.29 Answer 1

2020 x 790.00 = 1600000 Answer 1.60 x 106

50.0 / 0.020 = 2500 Answer 2500

50.0 / 0.02000 = 2500 Answer 2.50 x 103