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

Math for LifeTOPIC 1: UNITS AND CONVERSIONS / Page 3The units on the LHS (J) are the same as in the units on the RHS (also J). The unitsbalance. The equation is set up correctly.CHECKING EQUATIONS SHORTCUT:Always write down units.Cancel and check that units balance.To convert among units, you need to pick an appropriate fraction by which to multiplythe LHS. How do you do that?UNITS 1.2: Converting Among Units: A Five-Step PlanThe key to getting conversions right is to balance units of measurement, using thefollowing basic ideas:When two measures are equal, one divided by the other has a magnitude of one.EXAMPLES:1.00 meter = 1.09 yardsso,1m= 1109 . ydor equivalently:109 . yd1100 . m =A fraction like this is called a unit fraction (in this case, the word unit refers to the “1”).Multiplying by a unit fraction is like multipyling by 1; that is, multiplying by a unitfraction does not change the magnitude of your measure, only its units. So, if you wantto convert units without changing the magnitude, you can multiply by unit fractions.EXAMPLE:Convert 10 meters to yards.109 . yd10.0m× = 10.9yd100 . mThese units balance.BACKTOCNEXT