Converting mm, cm, m and km with Decimals

Four length units, three steps between them. A kilometre is a thousand metres; a metre is a hundred centimetres; a centimetre is ten millimetres. Going down the ladder to a smaller unit multiplies, going up to a bigger unit divides, and the multiplying and dividing is the digit-sliding from the decimals lesson. The check is that the number and the unit move in opposite directions: fifteen hundred centimetres is fifteen metres, a bigger unit and a smaller number. If your number grew when you went to a bigger unit, you went the wrong way.

Going down the ladder with a decimal is multiplying, so the digits slide left. Two point three five kilometres times a thousand is two thousand three hundred and fifty metres. Four point five metres is four hundred and fifty centimetres, and four thousand five hundred millimetres — two steps, or a thousand in one go. Check the size: a kilometre is a long way, so two point three five of them should be thousands of metres, not two hundred and thirty-five.

Going up the ladder divides, so the digits slide right. Fifteen hundred centimetres divided by a hundred: two columns, fifteen metres. Not one point five, not a hundred and fifty. Eighty-five centimetres is zero point eight five metres. Three thousand and forty metres divided by a thousand is three point zero four kilometres — the zero in the middle stays where it is. When the test asks which of several measurements equals fifteen hundred centimetres, count the columns and the answer is fifteen metres.

Mixed units are two numbers describing one length: two kilometres and three hundred and fifty metres is two thousand three hundred and fifty metres, or two point three five kilometres. Three kilometres and forty metres is three point zero four — the forty is only forty. To add or compare, get everything into one unit first: one point two metres plus eighty-five centimetres is a hundred and twenty plus eighty-five centimetres, two hundred and five. Working in the smaller unit keeps the arithmetic in whole numbers; convert back at the end only if the question asks.

Lengths in different units cannot be compared by their numbers. Zero point nine kilometres, nine hundred and fifty metres, eighty-five thousand centimetres, nine thousand five hundred millimetres: convert them all to metres — nine hundred, nine hundred and fifty, eight hundred and fifty, nine and a half — and nine hundred and fifty metres is the longest, even though eighty-five thousand is the biggest number on the page. Pick the unit most of them already use, convert the rest, then compare. Quiz and exercises now.