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Significant Figures 1.004 4.5678 32.000 600 2.45 0.5008 7 9.99999 8

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Measurement always involves some estimating. A better instrument allows for better measurements, recorded as a greater number of significant figures (digits).

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Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated. These are the SIGNIFICANT FIGURES. 3.23.2 certain estimated 3

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Rules for Significant Figures

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2. All zeroes between non-zero digits are significant. 50407 (5 sig figs) 8.001 (4 sig figs) 1. All non-zero digits are significant. 374 (3 sig figs) 8.1 (2 sig figs) 3. Leading zeroes are NOT significant. 0.54 (2 sig figs) 0.0098 (2 sig figs)

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4. Trailing zeroes are significant ONLY if there is a decimal point. 2370 (3 sig figs) 16000 (2 sig figs) 160.0 (4 sig figs) 000.1800 (4 sig figs) Always LOOK FOR A DECIMAL

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To avoid confusion, scientists commonly use SCIENTIFIC NOTATION. ALL digits in scientific notation are SIGNIFICANT 6.02 x 10 23 1.Move the decimal so it is behind the first non-zero digit. 2.Count the number of places that you moved the decimal - to the left is +, right is -

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2380002.38 x 10 5 0.00525.2 x 10 -3 1.5 x 10 4 15 000 6.35 x 10 -4 0.000635 1.103,000 2.1,236,000 3.42.0 4.0.00000021 5. 0.000238 1.03 x 10 5 1.236 x 10 6 4.20 x 10 1 2.1 x 10 -7 2.38 x 10 -4

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0-4: round down 5 -9: round up Rounding Rules 0.00533 (2 sig figs) 0.0053 426.3 (3 sig figs) 426 1890 (1 sig fig) 2000 0.0296 (2 sig figs) 0.030

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Addition and Subtraction Multiplication and Division Rules for

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You can only give an answer that is as accurate as your least accurate number.

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Add or subtract Count digits to the right of the decimal. Round the answer to match the value with the LEAST number of decimal places. Answer = 143.9 least number of decimal places 12.0 + 131.59 + 0.2798 = 143.8698

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Multiply or divide Answer is rounded to contain the same number of sig figs as the value with the LEAST. 51.3 × 13.75 = 705.375 The answer, with significant figures, is 705.

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DO NOT round for each calculation. When performing multiple calculations, use the rule of the final calculation to round the answer. (0.3012 + 0.2)(3.6) = ? (0.5)(3.6) = 1.8 = 2 (0.5012)(3.6) = 1.80432 = 1.8

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