What are the best strategies for identifying where to begin unit conversions?
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To help, I have my students ask themselves this question: are ending up with a unit that is bigger or smaller? In the case of the 3 kilograms, we are ending up with grams, which are smaller than the kilograms we started with. So since we are “breaking apart” the big kilograms into smaller grams, we multiply 3 x 1000 to get 3,000 grams. Multiplying gives us more, and we have more in the end if our unit gets smaller.
And this also works in reverse. Say we start with 3,000 grams and need to know how many kilograms that is. 1,000 grams still equal 1 kilogram, but this time we are “trading in” our smaller grams for lager kilogram at the end. So this tells us to divide 3,000 by 1,000 to get 3 kilograms. Dividing gives us less, and we have less in the end if our unit gets bigger.
And this also works in reverse. Say we start with 3,000 grams and need to know how many kilograms that is. 1,000 grams still equal 1 kilogram, but this time we are “trading in” our smaller grams for lager kilogram at the end. So this tells us to divide 3,000 by 1,000 to get 3 kilograms. Dividing gives us less, and we have less in the end if our unit gets bigger.
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