Measurement: Significant Figures

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Significant Figures Significant Figures (sig. figs.): the number of digits that carry meaning contributing to the precision of a measurement or calculated data.

Significant Figures The significance of a digit has to do with whether it represents a true measurement or not. Any digit that is actually measured or estimated will be considered significant. Placeholders, or digits that have not been measured or estimated, are not considered significant.

Significant Figures There are 5 rules to determine which digits in a measurement or number are significant or not.

Rules for Significant Figures Rule #1: All non-zero digits (1-9) are significant. For example: 453 number of sig figs______ 345.21 number of sig figs______

Rules for Significant Figures Rule #2: Zeros between non-zero digits are significant. For example: 12.007 number of sig figs______ 3008007 number of sig figs______

Rules for Significant Figures Rule #3: Zeros to the left (“leading” zeros) of the first non-zero digit are NOT significant. For example: 1.02 number of sig figs______ 0.12 number of sig figs______ 0.00127 number of sig figs______ 0.00040301 number of sig figs______

Rules for Significant Figures Rule #4: If a number ends in zeros (“lagging” zeros) to the right of the decimal point, those zeros are significant. For example: 2 number of sig figs______ 2.0 number of sig figs______ 2.00 number of sig figs______ 2.000 number of sig figs______ {This signifies greater precision.}

Rules for Significant Figures Rule #5: If a number ends in zeros (“lagging” zeros), the zeros to the right are NOT significant IF there is NO decimal point present. For example: 47100 number of sig figs______ 20060 number of sig figs______ 40000 number of sig figs______

Sig. Figs. Practice Ex 1) 0.020110 Ex 2) 730800 1) 48001 2) 9807000 1) 48001 2) 9807000 3) 0.008401 4) 40.500 5) 64000 6) 64000. 7) 64000.00 8) 0.0107050 Ex 1) 0.020110 (5 sig. figs.) Ex 2) 730800 (4 sig. figs) 1) 48001 (5 sig. figs.) 2) 9807000 (4 sig. figs.) 3) 0.008401 (4 sig. figs.) 4) 40.500 (5 sig. figs.) 5) 64000 (2 sig. figs.) 6) 64000. (5 sig. figs.) 7) 64000.00 (7 sig. figs.) 8) 0.0107050 (6 sig. figs.)

Calculations with Sig Figs Add and subtract: Answer gets rounded based on the fewest decimal places from question Example: 334.540 + 198.9916 533.6316 The last 6 isn’t significant because the fewest decimal places in the Q is the third

Calculations with Sig Figs Multiply and Divide: Answer gets rounded to fewest significant figures from the question 44 x 20 = 880 Round to 900 because one of the values in the question only has one sig fig

Answers to Significant Figure Calculation Practice 2) 3.4 g/ml 3) 4) -0.12 m 5) 450. cm 6) 0.28 m/s 7) 332.107 kg 8) 900 m