Math for Life - Life: The Science of Biology, Seventh ... - WH Freeman

Math for LifeTOPIC 1: UNITS AND CONVERSIONS / Page 9So, make the first fraction equal to 1 by relating grams to milligrams.Now, solve:10 . mg × ⎛ ? mol⎝ ⎜ 1g ⎞⎟ × ⎛ mg⎠⎝ ⎜1mol ⎞⎟ =310 58.44g⎠10 . mg × ⎛ 17 . 10 5 mol⎝ ⎜ 1g ⎞⎟ × ⎛ mg⎠⎝ ⎜1mol ⎞−⎟ = ×310 58.44g⎠This example had two different dimensions ⎯amount (moles) and mass (grams andmilligrams). This technique works no matter how many different dimensions thereare. As long as you multiply by 1, you are safe. For more examples, see the SOLU-TIONS section.CONVERSIONS SHORTCUT1. Write an equation.2. Count units.3. Insert that many fractions.4. Make units cancelable.5. Make fractions =1, then calculate.UNITS 1.4: Units Raised to PowersWhat if you want to convert m 2 to mm 2 ? These units are both squared. Here is ahandy technique for converting units that are raised to powers.The Point: Use parentheses.1. Put parentheses around the units, but not around the exponent, on the LHSof the equation.5.0 (m) 2 = ? mm 2 ?BACKTOCNEXT