Question 1.8: A clinical laboratory found that a blood sample contained 0....
A clinical laboratory found that a blood sample contained 0.0026 g of phosphorus and 0.000 101 g of iron.
(a) Give these quantities in scientific notation.
(b) Give these quantities in the units normally used to report them—milligrams for phosphorus and micrograms for iron.
ANALYSIS Is the number larger or smaller than 1? How many places do you have to move the decimal point?
(b) We know from Table 1.6 that 1 mg = 1 \times 10^{-3} g , where the exponent is -3. Expressing the amount of phosphorus in milligrams is straightforward because the amount in grams (2.6 \times 10^{-3} g) already has an exponent of -3. Thus, 2.6 \times 10^{-3} g = 2.6 mg of phosphorus.
(2.6\times 10^{-3}\cancel{ g} ) ( \frac {1 mg}{1 \times 10^{-3}\cancel { g} })= 2.6 mgWe know from Table 1.6 that 1 \mu g = 1 \times 10^{-6} g where the exponent is -6. Expressing the amount of iron in micrograms thus requires that we restate the amount in grams so that the exponent is -6. We can do this by moving the decimal point six places to the right:
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 (Mm) = 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 (dL0 = 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 |