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Significant Figures

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

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

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

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.

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.

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.

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

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.

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

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.

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)

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

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

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

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

Step 2 Write number without zeros

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

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

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

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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