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Significant Figures

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What is a significant figure? There are 2 kinds of numbers: –Exact: the amount of money in your account. Known with certainty.

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What is a significant figure? –Approximate: weight, height—anything MEASURED. No measurement is perfect.

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When to use Significant figures When a measurement is recorded only those digits that are dependable are written down.

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When to use Significant figures –If you measured the width of a paper with your ruler you might record 21.7cm. To a mathematician 21.70, or 21.700 is the same.

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But, to a scientist 21.7cm and 21.70cm is NOT the same 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

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But, to a scientist 21.7cm and 21.70cm is NOT the same If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

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How do I know how many Sig Figs? Rule: All digits are significant starting with the first non-zero digit on the left.

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How do I know how many Sig Figs? Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

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How many sig figs? 7 40 0.5 0.00003 7 x 10 5 7,000,000 1 1 1 1 1 1

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How do I know how many Sig Figs? 2 nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

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How do I know how many Sig Figs? 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant. (showing how accurate the measurement is)

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How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 3 6

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Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

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The Distance From the Sun to the Earth 93,000,000

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Step 1 Move decimal left Leave only one number in front of decimal

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Step 2 Write number without zeros

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Step 3 Count how many places you moved decimal Make that your power of ten

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The power of ten is 7 because the decimal moved 7 places.

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93,000,000 --- Standard Form 9.3 x 10 7 --- Scientific Notation

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Practice Problem 1)98,500,000 = 9.85 x 10 ? 2)64,100,000,000 = 6.41 x 10 ? 3)279,000,000 = 2.79 x 10 ? 4)4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6

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