This is an important skill which children need to master, especially now that we live in a metric, rather than an Imperial measuring world. You will see how important when you look at the section on converting metric units.

Nevertheless I find that many children are not taught how to do this properly at an early age and as such learn bad habits. It is amazing how many children tell me that they have been taught to multiply by 10 by adding a zero onto the end of the number, and two zeros when multiplying by 100 etc. This is fine when dealing with whole numbers, but when we start multiplying decimals we get responses such as this:- 2.7 x 10 = 2.70 or 0.56 x 100 = 0.5600

And you can't blame the children, as they are only doing what they have been taught to do! This is the danger of children learning rules without understanding the mathematical processes behind them, and of teachers not knowing the correct rules themselves.

The easiest way to demonstrate the rules is to get children to write out the standard mathematical column headings starting with the thousands column, then the hundreds, tens, units, tenths, hundredths and thousandths. Into these columns they write the number 0.018. Next get a calculator and multiply 0.018 by 10. They will get the answer 0.18, which they also write in the correct columns. Now multiply this answer by 10 again to get 1.8, again to get 18, again to get 180 etc. The children should thus notice that when numbers are multiplied by 10 the digits simply stay together, but all move 1 column to the left.

You can start again, but multiply by 100 or 1000 instead. Can they say what the rules are this time? How about starting with 4500 and dividing by 10 repeatedly. They should see that this time the digits stay together but move one column to the right. The rules are therefore:

To multiply by 10 the digits stay together and move 1 column to the left.

To multiply by 100 the digits stay together and move 2 columns to the left.

To multiply by 1000 the digits stay together and move 3 columns to the left.

To divide by 10 the digits stay together and move 1 column to the right.

To divide by 100 the digits stay together and move 2 columns to the right.

To divide by 1000 the digits stay together and move 3 columns to the right.

To help remember the rules there is a poster below, which can be downloaded and printed off. It was designed and created for me by J Foreman.

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