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Sig. Figs. Essential Questions: What are sig. figs? How are they used in science? What rules are used to govern sig. figs. when doing calculations?

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What are Sig. Figs? They are those digits that carry meaning contributing to a measurement or values accuracy. They are those digits that carry meaning contributing to a measurement or values accuracy. Sig. Figs. is short for significant figures or digits. Sig. Figs. is short for significant figures or digits.

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The Rules to follow when identifying which digits are significant. 1. ALL non-zero numbers are always significant. Ex. 1, 234 cm or g 2. Zeros between non-zero numbers are always significant. Ex. 2, 008 m 3. Zeros to the left are never significant. Ex kg (You only count the 5 and 2 as significant.)

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The Rules cont. 4. Zeros to the right of a non-zero number when a decimal is involved are significant. Ex mL (The decimal makes the last zero significant.) or g (The three zeros after the five are significant, while the zero to the left is not.) 25,000 g (Only the 2 and 5 are significant, because there is NO decimal present!) 25,000 g (Only the 2 and 5 are significant, because there is NO decimal present!) 5. All Exact values are significant, even if they contain zeros. Ex. 1,760 yds = 1.0 miles 60 s = 1 min.

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Try some… Determine the number of sig. figs. in each value. Determine the number of sig. figs. in each value ,500 g m 3. 1,234, mL cm hg

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The Answers … 1. 4 (The zeros after the 5 do not count, because no decimal is present. The first two zeros are counted, because they are in-between non-zero numbers.) 2. 8 (All of the digits are significant.) (All digits are significant.) 4. 1 (Only the 1 is significant, because there is no decimal to include the zeros.) 5. 3 (All the digits are significant; there is a decimal.)

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Rules to follow for calculations: When adding and subtracting, the number of sig. figs. is based on decimal placement. The original value with the fewest decimal places is the value that must be used for the final answer. (Normal rounding rules apply…5 or greater: round up; 4 or lower: round down) When adding and subtracting, the number of sig. figs. is based on decimal placement. The original value with the fewest decimal places is the value that must be used for the final answer. (Normal rounding rules apply…5 or greater: round up; 4 or lower: round down) Ex g g = g ~ g (2 dec.) (3 dec.) (3 dec.) (F.A. = 2 dec)

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Rules for Math (cont.) When multiplying and dividing, the answer must have the same number of sig. figs. as the original number with the least sig. figs. The key is to do the math, and then round at the end to the correct sig. figs. When multiplying and dividing, the answer must have the same number of sig. figs. as the original number with the least sig. figs. The key is to do the math, and then round at the end to the correct sig. figs. Ex. 5.0 cm x 5 cm = 25.0 cm 2 ~ 30 cm 2 Ex. 5.0 cm x 5 cm = 25.0 cm 2 ~ 30 cm 2

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