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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.
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.
21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.
If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.
Rule: All digits are significant starting with the first non-zero digit on the left.
Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.
7 40 0.5 0.00003 7 x 10 5 7,000,000 11 11 11 11 11 11
2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.
3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.
3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.
1.2 2100 56.76 4.00 0.0792 7,083,000,000 22 22 44 33 33 44
3401 2100 2100.0 5.00 0.00412 8,000,050,000 44 22 55 33 33 66
Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.
2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm 7.432cm + 2cm = 9.432 round to 9cm
Rule: When multiplying or dividing, the result can have no more significant digits than the least reliable measurement.
56.78 cm x 2.45cm = 139.111 cm 2 Round to 139cm 2 75.8cm x 9.6cm = ?
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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