1.2 Using the place value
Writing numbers in place-value columns gives an easy way of multiplying by 10, 100, 1000 and so on. Have a look at the place value table again.
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Units |
Notice that moving all the digits one column to the left in the table (and adding a zero to the units column) is the same as multiplying by ten; for instance, ten tens are a hundred, ten hundreds are a thousand. If you move two columns to the left, you multiply by a hundred; for instance, a hundred tens are a thousand. Moving three columns to the left is equivalent to multiplying by a thousand, and so on.
Example 2
After local government re-organisation a new council expects to receive cash payments in ten instalments from about 26 000 households. In order to negotiate the cash collection at post offices it needs to know how many payments are made altogether in a year. How many are there likely to be?
Answer
The total number of payments is the number of households times the number of payments per household, i.e. 26 000 × 10. This can be worked out by moving all the digits of 26 000 one place to the left, and adding a zero at the end:
| M | H Th | T Th | Th | H | T | U | ||
| 2 | 6 | 0 | 0 | 0 | ||||
| = | 2 | 6 | 0 | 0 | 0 | 0 | ||
| Digits moved one place to the left | Extra zero added | |||||||
So 26 000 × 10 = 260 000.
A total of 260 000 cash payments should be expected.