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 precisionWe measure to the last known calibration, and estimate the unknown.
5 Significant Figures – The Rules 1. Nonzero numbers 1 – 9 are always significant.Examples:1 meter sig fig92 liters sig figs34578 grams sig figs
6 Significant Figures – The Rules 2. Imbedded zeros (zeros between nonzero numbers) are always significant.Examples:202 cm 3 sig figs10509 mL 5 sig figs2039 kg 4 sig figs90009 g 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:g 3 sig figsmm 4 sig figsL 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 figs100 dg 1 sig fig8900 km 2 sig figs8900. km 4 sig figs
9 Exact NumbersAn exact number is a number that cannot be changed. (Cannot be halved or split up)Ex. 2 atoms, 1 proton, a hundred dollar billWe include most conversion factors as exact numbersEx. 1m = 100 cmWhen you work with exact numbers, you consider them to have infinite sig figs.(You don’t have to worry about them!)
10 0.00770800 RECAP #1 Leading Zeros Imbedded Zero after the decimal Nonzero numbers Trailing Zerosafter the decimal
25 Rounding NumbersIf you have to round and the number you are looking to round is less than 5, don’t round.Example:214round to 2 s.f.Answer = 210
26 Rounding NumbersIf you have to round and the number you are looking to round is 5 or greater, round up.Example:215round to 2 s.f.Answer = 220
27 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.
28 YOU ARE LOOKING AT PLACES AFTER THE DECIMAL NOT SIGNIFICANT FIGURES!
29 Example:= 6.0You look for the least number of PLACES after the decimal.2.00 = 2 places after the decimal4.0 = 1 place after the decimalYour answer can only have one place after the decimal.
30 2.0 + 4 = 6 Example: 2.0 = 1 place after the decimal 4 = no places after the decimalYour answer can not have any places after the decimal.
31 Example:– ==0.055= 5 places after the decimal0.001 = 3 places after the decimalYour answer can only have 3 places after the decimal.