Question 1.4: The HIV-1 virus particles seen in the margin photo on p. 48 ...
The HIV-1 virus particles seen in the margin photo on p. 48 are very small, on the order of 0.000 000 120 m in diameter. Express this value using scientific notation and using an appropriate numerical prefix to modify the basic unit.
ANALYSIS The number is significantly less than one, so when we convert to scientific notation we should have a number with a negative exponent. We can use the value of that exponent to identify the appropriate numerical prefix.
To convert to scientific notation we have to move the decimal place to the right by seven places, so 0.000 000 120 m = 1.20 \times 10^{-7} m. From Table 1.6, the closest numerical prefixes are micro (10^{-6}) or nano (10^{-9}) . If we moved the decimal place six places to the right we would obtain:
0.000 000 120 m = 0.120 \times 10^{-6} m = 0.120 micrometers (\mu m)
If we move the decimal place nine places to the right we obtain:
0.000 000 120 m = 120 \times 10^{-9 }m = 120 nanometers (nm)
table 1.6 Some Prefixes for Multiples of Metric and SI Units
| Prefix | Symbol | Base Unit Multiplied By | Example |
| mega | M | 1,000,000 = 10^{6} | 1 megameter (M m) = 10^{6} m |
| kilo | k | 1000 = 10^{3} | 1 kilogram (kg) = 10^{3} g |
| hecto | h | 100 = 10^{2} | 1 hectogram (hg) = 100 g |
| deka | da | 10 = 10^{1} | 1 dekaliter (daL) = 10 L |
| deci | d | 0.1 = 10^{-1} | 1 deciliter (dL) = 0.1 L |
| centi | c | 0.01 = 10^{-2} | 1 centimeter (cm) = 0.01 m |
| milli | m | 0.001 = 10^{-3} | 1 milligram (mg) = 0.001 g |
| micro | \mu | 0.000 001 = 10^{-6} | 1 micrometer (\mu m) = 10^{-6} m |
| nano | n | 0.000 000 001 = 10^{-9} | 1 nanogram (ng) = 10^{-9} g |
| pico | p | 0.000 000 000 001 = 10^{-12} | 1 picogram (pg) = 10^{-12} g |
| femto | f | 0.000 000 000 000 001 = 10^{-15} | 1 femtogram (fg) = 10^{-15} g |