Units & compound-unit conversion

Every conversion in this topic is the same move wearing a different uniform: 1 km = 1000 m, 1 kg = 1000 g, 1 l = 1000 ml, 1 m = 100 cm. Going to a smaller unit means there will be more of them, so you multiply; going to a bigger unit means there will be fewer, so you divide. Ask yourself which way the answer should go before you touch the numbers — that one question catches most of the marks people drop here. A compound measurement such as 4 kg 60 g is simply two measurements written side by side, so convert one part, leave the other alone, and add. And when two compound measurements are added or subtracted, change both into the smaller unit first: 60 g and 950 g will carry into a whole kilogram, and no amount of care with the columns will save you if the units do not match.

Worked example

Problem Express 4 kg 60 g in grams.

Split the measurement into its two parts: 4 kg and 60 g. Only the first one has to change.
Since 1 kg = 1000 g, the 4 kilograms are 4 × 1000 = 4000 g.
Add the leftover grams back on: 4000 + 60 = 4060 g.
Watch out 4 kg 60 g is not 4060 g because the digits look like that — it is 4060 g because 60 g were added to 4000 g. Written as a decimal it is 4.06 kg, not 4.6 kg: the 0 is holding the tenths place.
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