4 Metric Conversions
Now that you’ve practiced writing metric equalities, it’s time to use them in conversions. Going from a prefixed unit to no-prefix unit (or vice-versa) is pretty straightforward.
Example 4.1
Convert 4560 J to kJ.
Answer: Recall the equality that relates the prefixed unit to the no-prefix unit, 1000 J = 1 kJ, in this case.
Always start with the given quantity, not the conversion factor. Then use the equality as a conversion factor in such a way that the units on the given quantity cancel.
[latex]4560 J *\frac{1 kJ}{1000 J}= 4.56 kJ[/latex]
When going from one prefixed unit to another prefixed unit, it is best to do the conversion in two steps. First, go from the prefixed unit of the given quantity to the no-prefix unit, using the prefix definition you have memorized. Then, go from the no-prefix unit to the prefixed unit you desire in the end, using the definition you have memorized. Two steps are necessary, because you have memorized each prefix relative to the no-prefix quantity, not relative to another prefix. See the following example for an illustration.
Example 4.2
Convert 8.75 x 107 mm to km.
Answer: The conversions needed are relating the prefixed unit to the no-prefix unit:
1000 mm = 1 m and 1000 m = 1 km
Start with the given quantity, and use the mm to m conversion first, then the m to km conversion.
[latex]8.75x10^7 mm*\frac{1m}{1000mm}*\frac{1km}{1000m}=87.5 km[/latex]
