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Published byBaldric Hunt Modified over 5 years ago

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There are 2 kinds of numbers: Exact: the amount of money in your account. Known with certainty. Approximate: weight, height— anything MEASURED. No measurement is perfect.

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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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21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

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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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Rule: All digits are significant starting with the first non-zero digit on the left.

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Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

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7 40 0.5 0.00003 7 x 10 5 7,000,000 11 11 11 11 11 11

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2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

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3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

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3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

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1.2 2100 56.76 4.00 0.0792 7,083,000,000 22 22 44 33 33 44

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3401 2100 2100.0 5.00 0.00412 8,000,050,000 44 22 55 33 33 66

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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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2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm 7.432cm + 2cm = 9.432 round to 9cm

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Rule: When multiplying or dividing, the result can have no more significant digits than the least reliable measurement.

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56.78 cm x 2.45cm = 139.111 cm 2 Round to 139cm 2 75.8cm x 9.6cm = ?

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1) 5.40 ____ 6) 1.2 x 103 ____ 2) 210 ____ 7) 0.00120 ____ 3) 801.5 ____ 8) 0.0102 ____ 4) 1,000 ____ 9) 9.010 x 10- 6 ____ 5) 101.0100 ____ 10) 2,370.0 ____

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