Question 2.28: Unit Conversion Involving Units Raised to a Power How many s......
Unit Conversion Involving Units Raised to a Power
How many square meters are in 1.0 km^2?
Step-by-Step
GIVEN: 1.0 km^2
FIND: m^2
SOLUTION MAP
RELATIONSHIPS USED
1 km = 1000 m (Table 2.2)
SOLUTION
1.0 km^2 \times \frac{(1000 m)^2}{(1 km)^2}= 1.0 \cancel{km^2} \times \frac{1 \times 10^6 m^2}{1 \cancel{km^2}}
= 1.0 \times 10^6 m^2
The units are correct. The answer makes physical sense.
A square meter is much smaller than a square kilometer, so the number of square meters should be much larger than the number of square kilometers.
Table 2.2
| SI Prefix Multipliers | ||||
| Prefix | Symbol | Meaning | Multiplier | |
| tera- | T | trillion | 1,000,000,000,000 | (10^{12}) |
| giga- | G | billion | 1,000,000,000 | (10^{9}) |
| mega- | M | million | 1,000,000 | (10^{6}) |
| kilo- | k | thousand | 1,000 | (10^{3}) |
| hecto- | h | hundred | 100 | 10^{2} |
| deca- | da | ten | 10 | 10^{1} |
| deci- | d | tenth | 0.1 | (10^{-1}) |
| centi- | c | hundredth | 0.01 | (10^{-2}) |
| milli- | m | thousandth | 0.001 | (10^{-3}) |
| micro- | µ | millionth | 0.000001 | (10^{-6}) |
| nano- | n | billionth | 0.000000001 | (10^{-9}) |
| pico- | p | trillionth | 0.000000000001 | (10^{-12}) |
| femto- | f | quadrillionth | 0.000000000000001 | (10^{-15}) |
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