Multiplying and dividing by 10, 100 and 1000
When you multiply by 10, every digit moves one place to the left; when you divide by 10, one place to the right. See it on the place-value chart, first with whole numbers, then with decimals.
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- Russia: grade 4
Guide
On the place value chart, each place is worth 10 times the place on its right. So when we multiply by 10, every digit moves one place to the left and becomes worth 10 times as much. The empty ones place gets a 0 to hold it.
The ×10 button slides all the digits one place left together, and ÷10 slides them one place right. Multiplying by 100 is multiplying by 10 twice; by 1000, three times.
"Just add a zero" is a shortcut that only works for whole numbers, and only because the digits have moved. It goes wrong with a decimal (decimal number): 3.45 and 3.450 are the same number! With decimals, the digits move across the decimal point.
The decimal point stays where it is, between the ones and the tenths. It's the digits that move.