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chapter 2

# chapter 2 - A number in scientific notation has the number...

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A number in scientific notation has the number ten raised to a power, either positive or negative. For example: 10 0 = 1 10 1 = 10 10 2 = 100 10 3 = 1000 10 -1 = 0.1 10 -2 = 0.01 10 -3 = 0.001 A number in scientific notation has two parts, a coefficient (a number with one integer to the left of a decimal point) and the number 10 raised to a power. Some examples: 1 x 10 0 1 x 10 1 , 1 x 10 2 , 1 x 10 3 , 1 x 10 -1 , 1 x 10 -2 , 1 x 10 -3

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Numbers written in Scientific Notation 12 = 1.2 x 10 1 26.7 = 2.67 x 10 1 87.329 = 8.7329 x 10 1 378.76 = 3.7876 x 10 2 728632.2197 = 7.286322197 x 10 5 2.6432 = 2.6432 x 10 0 0.216 = 2.16 x 10 -1 0.0009426 = 9.426 x 10 -4
Scientific Notation Number as Ordinary Number 4.67 x 10 1 = 46.7 8.95432 x 10 3 = 8954.32 64.92 x 10 2 = 6492 8.3421 x 10 -1 = 0.83421 9.5289 x 10 -4 = .00095289 4.769 x 10 -2 = 0.04769 5.729 x 10 0 = 5.729 6.7894 x 10 -0 = 6.7894

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Category Base Unit Abbreviation Length meter m Mass gram g Volume liter L Temperature degree Celsius e C
Prefix Symbol Exponent Multiplier (factor) centi- c 10 - 2 1/100 (one hundredth) milli- m 10 - 3 1/1000 (one thousandth) kilo- k 10 3 1000 (one thousand)

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quantity sought = quantity given x conversion factor(s) 2 conversion factors per equivalence (i.e., equality) e.g 1 ft = 12 in ; (1 ft/12 in) and (12 in/1 ft), and 1 ft = 30.5cm (1 ft/30.5 cm) and (30.5 cm/1 ft) (English/English) How many inches in 2 miles? ans: ? in = 2 mi x (5280ft/1mi) x (12in/1ft) = 126,720 in (metric/metric) How many millimeters in 1 kilometer ? ans: ? mm = 1km x (1000m/km) x (100cm/m) x (10mm/cm) =1,000,000mm (English/metric) How many centimeters in 2 miles? ans: ?cm = 2mi x (5280ft/mi) x (30.5cm/ft) = 322,080cm
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chapter 2 - A number in scientific notation has the number...

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