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Ms. Pollock 2013 - 2014

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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

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2.4 Significant Figures Observation List AObservation List B 22.41359 m22.4 m 22.37899 m22.4 m 22.42333 m22.4 m 22.39414 m22.4 m *Accounts for limitations of measuring device *Rounded number (estimation)

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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.

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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.

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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

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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

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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 cm 112.2 cm Multiplication and Division Same number of significant figures as factor with least number of significant figures (3.556 cm) * (2.4 cm) = 8.5344 cm 2 = 8.5 cm 2

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