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Significant Figures Significant figures in a measurement includes all of the digits that are known, plus a last digit that is estimated. All measurements are approximations……. no measuring device can give perfect measurements without experimental uncertainty. The numbers reported in a measurement are limited by the measuring tool

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Read the bottom of the meniscus This cylinder is accurate to the ones place = 35 mL We can see that the meniscus falls right on the line for 35, so we estimate to the tens place = 35.0 mL

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Significant figures (sig figs) When we measure something, we can (and do) always estimate between the smallest marks. 21345 4.5 cm

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Significant figures (sig figs) The better marks the better we can estimate. Scientist always understand that the last number measured is actually an estimate. 21345 4.55 cm

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Significant figures (sig figs) The measurements we write down tells us how accurate the ruler is that we measured with 141 142 142.13cm

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Counting Significant Figures SF? 38.15 cm 5.6 ft 65.6 lb 122.55 m All non-zero digits are significant. ANSWERS 4 2 3 5

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Counting Significant Figures Any zero between nonzero digits are significant. SF? 50.8 mm 2001 mi 0.702 lb 0.00405 ANSWERS 3 4 3 THE SANDWICHED ZEROS

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Counting Significant Figures All zeroes to the left of nonzero digits are not significant. SF? 0.008 mm 0.0156 oz 0.0042 lb 0.000262 mL ANSWERS 1 3 2 3 PLACE HOLDERS, ONLY

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Counting Significant Figures Zeroes to the right of nonzero digits ARE significant if a decimal pt. is present. SF? 25.00 in. 0.0200 yr 1.0 gal ANSWERS 4 3 2 IF THEY WEREN’T SIGNIFICANT THEN WE WOULDN’T WRITE THEM

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Zeroes to the right of nonzero digits ARE NOT significant if a decimal pt. is absent. Counting Significant Figures SF? 25,000 in. 200 yr 48,600 gal ANSWERS 2 1 3 ONLY BEING USED AS PLACE HOLDERS

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Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 answer 26.5 one decimal place

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Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

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Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041

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