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A measured value Number and unit Example 6 ft.

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Accuracy How close you measure or hit a true value or target

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Precision How many times you measure the same quantity or how many times you hit the exact same position

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Significant Figures Measured digits with no known certainty. + or – an amount Uncertain last digit Rules to know how many significant figures are in a number (sig. figs.) 35.3 could be 35.3 (+ or -.1), so could have measured it at 35.2 or 35.4. Depends on how you round it up or down.

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0 Rule All non zero numbers are significant Place holders are not significant Measured zero is significant

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Rule 1 Zeros between nonzero numbers are significant 507.2 = 4 sig. figs. 1.0048 = 5 sig. figs. These numbers were all actually measured.

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Rule 2 Zeros to the right of a decimal and in front of the number are not significant.0048 = 2 sig. figs. First two numbers were not actually measured, they are place holders. 1.0048 = 5 sig. figs. All of these numbers were measured.

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Rule 3 Zeros to the right of a decimal and end of the number are significant 3.620 = 4 sig. figs. Because all the numbers had to have been measured. Could have been 3.619 or 3.621, so 0 at the end is the uncertainty number, no other reason to have put it there unless it was measured and rounded.

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Rule 4 Zeros at the end of a whole number may or may not be significant. 170 pounds. No one knows if the last number was measured or estimated. 1.70 x 10 2 means all the numbers are significant and the last one is uncertain. 1.7 x 10 2 means that all the numbers are accurate and were measured.

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Adding sig. figs How many numbers to the right of a decimal that you have in your answer, depends on the measured number with the least amount of sig. figs. 5.36 + 2.4 = 7.76 = 7.8 = 2 sig. figs. Same with subtraction

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Rounding off Rules when adding or subtracting First non-significant number at the end of the number is extra, you don’t need it. Rule 1 –above 5 = +1 Rule 2 –under 5 = use the same number Rule 3 –if it is 5 and the next number is 1-9, +1 -if it is 5 and the next number is 0 or not there, look at the number before the 5. If it is even then use the same number, if it is odd, then +1. 7.225 = 7.22 7.275 = 7.28

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Multiplication Rules No more numbers in your answer than is in the least sig. fig. number that you measured. 203.5 x 4.0 means your answer should have only 2 sig. figs. 203.5 x 4.0 = 814.00 Round the 4 down = 810 and the 0 is a place holder so 8.1 x 10 2 = 2 sig. figs.

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532.4 x 13.7 = 729.38 = 729 = 3 sig. figs.

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