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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. Significant = replaceable A number is significant because it can be replaced by another number in a measurement 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 10509 mL 2039 kg 90009 g 3 sig figs 5 sig figs 4 sig figs 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 0.3700 mm 0.00101 L 3 sig figs 4 sig figs 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 100 dg 8900 km 8900. km 3 sig figs 1 sig fig 2 sig figs 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!) RECAP #1 Leading Zeros Imbedded Zero 0.00770800 Nonzero numbers Trailing Zeros after the decimal 6 significant figures RECAP #2 Leading Zeros (none) Imbedded Zero 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 dollars 1 sig fig Rule 1, 5 207 donkeys 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 2 10 hm 3 sig figs Rule 1, 4 2.2 x 34 10 atoms 2 sig figs Rule 1 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