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Significant Figures

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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 certain estimated 3

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Rules for Significant Figures

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2. All zeroes between non-zero digits are significant (5 sig figs) (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 (2 sig figs) (2 sig figs)

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4. Trailing zeroes are significant ONLY if there is a decimal point (3 sig figs) (2 sig figs) (4 sig figs) (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 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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x x x x , ,236, x x x x x 10 -4

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0-4: round down 5 -9: round up Rounding Rules (2 sig figs) (3 sig figs) (1 sig fig) (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 = least number of decimal places =

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Multiply or divide Answer is rounded to contain the same number of sig figs as the value with the LEAST × = 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. ( )(3.6) = ? (0.5)(3.6) = 1.8 = 2 (0.5012)(3.6) = = 1.8

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