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Significant Figures

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What is a significant figure? There are 2 kinds of numbers: 1. Exact : Known with certainty. Example: the number of students in this room 2. Approximate: anything MEASURED. Example: Mass, volume, length, weight, height 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 21.700 cm to a scientist means the measurement is accurate to within 1/1000 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 1 : All non zero digits are significant. Example: 1,246 (4 sig figs)

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How do I know how many Sig Figs? Rule 2 : Any zeros between significant digits are also significant. Example: 1,206 (4 sig figs)

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How do I know how many Sig Figs? Rule 3 : If the number does not contain a decimal point, any zeros to the right of a nonzero number are NOT significant Example: 1,200 (2 sig figs)

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How do I know how many Sig Figs? Rule 4 : If zeros are at the end of a number that has a decimal, the zeros are significant. Example: 1,200. (4 sig figs)

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How do I know how many Sig Figs? Rule 5 : If a value has no significant digits to the left of a decimal point, any zeros to the right of the decimal point before the non zero numbers (leading zeros) are not significant. Example: 0.0012 (2 sig figs)

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How do I know how many Sig Figs? Rule 6 : Zeros that are found after non zero numbers to the right of a decimal point are significant (trailing zeros) Example: 0.1200 (4 sig figs)

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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 many sig figs here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 2 4 3 3 4

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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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What about calculations with sig figs? Rule : When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

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Add/Subtract examples 2.45cm + 1.2cm = 3.65cm round to = 3.7cm 7.432cm + 2cm = 9.432 round to 9cm

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Multiplication and Division Rule : When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

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A couple of examples 56.78 cm x 2.45cm = 139.111 cm 2 round to 139cm 2 75.8cm x 9.60cm = ? 728 cm 2

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Have Fun Measuring and Happy Calculating!

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