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Significant Figures

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In science, measured values are reported in terms of significant figures. Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

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If we look back at this figure from yesterday, the digits we are certain of are 36. The final measurement, depending on who is reading the cylinder, could be 36.5, 36.6, and even 36.7 mL.

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**Rules for Determining Significant Figures**

Rule #1. Nonzero digits are always significant. 6.24g ________sig figs mm _______ sig figs kg _______ sig figs 67 seconds _______ sig figs

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**Rule #2 Zeroes appearing between nonzero digits are significant.**

_________ sig figs 40.7 _________ sig figs _____sig figs 2300.5________ sig figs

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**Rule # 3 Leading zeroes do not count as significant figures 0**

Rule # 3 Leading zeroes do not count as significant figures 0.7 g________ sig figs L____ sig figs dL ______ sig figs 0.15m________sig figs

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Rule #4 Zeroes at the end of a number are significant only if the number contains a decimal point. 50 g________ sig figs 2850m______ sig figs 7.50mm______ sig figs mL______sig figs kg____sig figs

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Rules for Rounding If the digit immediately to the right of the last significant figure you want to retain is: Less than the last significant digit should stay the same. Example: Round m to 3 significant figures. Since the 2 is less than 5, you should round to __________ m

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**Round 42.88 g to 3 significant figures.**

If the digit immediately to the right of the last significant figure you want to retain is: 5 or greater the last significant figure should increase by 1. Example: Round g to 3 significant figures. Since 8 is greater than 5, you should round to __________ g

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**Addition or Subtraction**

Rule #1: Whenever you add or subtract measurements, your answer should have as many DECIMAL PLACES as the measurement with the LEAST number of DECIMAL PLACES. EXAMPLE: g g = g 31.28 g

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Rule#2: Whenever you multiply or divide measurements, your answer should have as many SIGNIFICANT FIGURES as the measurement with the LEAST number of SIGNIFICANT FIGURES. EXAMPLE: cm × 5.5 cm = 7.381 cm2 7.4 cm2

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Study Check Carry out the following calculations and give the answer with the correct number of significant figures: / x 4.21

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