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

Math for LifeTOPIC 1: UNITS AND CONVERSIONS / Page 5You need µm in the denominator to cancel the µm on the LHS, andyou need pm in the numerator to balance the pm on the RHS.pm1µ m × ⎛ pm⎝ ⎜ ⎞⎟ × ⎛ ⎞µ m⎠⎝ ⎜ ⎟⎠= ?Step five:Make your fractions equal to 1. Do this by looking for relationshipsyou know. You could do this in at least two ways.[1] You know or can find out from consulting the table of PREFIXESlisted in REFERENCES, that 1 µm = 10 −6 m and 1 pm = 10 −12 m.You can use the information as follows to make useful unit fractions:−6If 10 m m then, 10 m −6= 1µ= 1.1µmand−121m pIf 10 m = 1pm then, = 1.−1210 mNow, fill in your equation:−610 11µm × m pm121µm× 10 m= pm−?or, equivalently,121m10 pmµ m × × =?pm610 µ m 1mNow, cancel both µm and m, solve, and you find that 1µm = 10 6 pm.[2] If you happen to know that 10 −6 µm = 1 pm, you can combineyour two unit fractions into a single unit fraction. Use one with µmin the denominator. That is, because−61pm1pm= 10 µ m,= 1−610 µ mBACKTOCNEXT