IB Chem IUncertainty in Measurement

Significant Figures

Significant Figures in Measurement

• A measurement in science has two meanings.• 1) A numerical value with the proper units• 2) The precision of the instrument being used.• Measured quantities contain all of the digits

that are known and one digit that is estimated (uncertain) plus the proper unit.

• The digits used to express a measured quantity are called significant figures.

Counting Sig Figs (Rules)

• 1. All nonzero numbers are significant. • ex. A) 3.246 has 4 sig figs, b) 754.891

has 6

• 2. Zeroes between nonzero digits and at the end of a number after the decimal point are significant.

• ex. A) 304.2 has 4 sig figs b) 4.70900 has 6 sig figs

Sig Figs Cont.

• 3. Zeros before the first nonzero digit and at the end of a number with out a decimal point are not significant.

• ex. A) 0.00045 has two , B) 8000 has one• General rule:• Start counting with the first nonzero digit and

count all digits until the last nonzero digit or the last zero ending the number after the decimal.

Examples – How many Sig Figs

• 1) 975 m 2) 0.090 l 3) 900.0 g

• 4) 900 g 5) 0.00073 m 6) 901 m

• 7) 3.760 x 10-3 g 8) 2.002 x 102 kg

Sig Figs in Calculations

• All calculations must be rounded off to the correct number of sig figs. Answers can only have the same number of sig figs as the least precise number in the problem.

• 130.57 km - round to 3 sig fig• 0.0552 mg – round to 1 sig fig• 1.789 x 106 – round to 2 sig figs

Significant Figures in Calculations

• Additional and Subtraction – Round answers to the same number of decimal places (e.g. tenths, hundreds, etc.) as the measurement with the least number of decimal places.

• 1) 34.6 + 1.8 + 12.33 meters =• 2) 1.20 + 1 meter =• 3) 1.0 + 1.001 + 01.0 g =

Multiplication and Division

• Round answer to the same number of sig figs as the measurement with the least number of sig figs.

• 1) 1.2 meters x 8 meters =

• 2) 3645 ml x 12.5 ml =

• 3) 1.2 mg x 2.30 mg x 2.30 mg =

Unlimited Significant Figures

There are two conditions in which measurements have an unlimited number of sig figs.

1) If the number is the result of counting, it is an exact measurement and has unlimited number of sig figs. The only number can be a whole number.

Unlimited Significant Figures

• 2) If the number is an exact defined quantity– 1 meter = 100.00000000… cm– 1 hour = 60.0000000… minutes– 5 chairs– 2 Humans