2.4 SIGNIFICANT FIGURES

Ms. Pollock

2013 - 2014

2.4 Significant Figures

Numbers in math class considered to be exact – produced by definition, not by measurement

Measurements not perfect Important to recognize and report

limitations

2.4 Significant FiguresObservation List A Observation List B

22.41359 m 22.4 m

22.37899 m 22.4 m

22.42333 m 22.4 m

22.39414 m 22.4 m

*Accounts for limitations of measuring device

*Rounded number (estimation)

2.4 Rules for Determining Significant Figures

Significant figures – significant digits; all digits that can be known with a certainty in a measurement plus an estimated last digit

Tracks limits of original measurement Write down all measurements, including

those of zero. Problem is knowing which zeros are

measured and which are place-holders.

2.4 Rules for Determining Significant Figures

1. All non-zero digits are significant.

2. All zeros between non-zero digits are significant.

3. All beginning zeros are not significant.

4. Ending zeros are significant if the decimal point is actually written in but not significant if the decimal point is an understood decimal.

2.4 Rules for Determining Significant Figures - Examples

1. 543 – three significant figures

22.437 – five significant figures

2. 7,004 – four significant figures

10.3002 – six significant figures

3. 0.00000075 – two significant figures

0.003003 – four significant figures

4. 100. – three significant figures

100 – one significant figures

1,050 – three significant figures

2.4 Significant Figures

Quality measuring instruments made as accurate as possible

Choice of measuring instrument determines unit of measure and number of significant figures

Significant figures used to report computational results with measurement

Rules for computations different depending on the type of calculation

2.4 Significant Figures Addition and Subtraction

Must not have any digits further to the right than the shortest addend (same number of decimal places as the smallest number of decimal places)

56.8885 cm + 8.30 cm + 47.0 Cm = 112.1885 cm112.2 cm

Multiplication and DivisionSame number of significant figures as factor with

least number of significant figures(3.556 cm) * (2.4 cm) = 8.5344 cm2 = 8.5 cm2