3.10 Multiply and divide by 10; the powers of 10
Are you ready?
Let's remember how the numbers are affected when we multiply and divide by 10.
Examples
Example 1
Find 8\times 10.
When we are multiplying our number by 10, it's the same as moving each of the digits to the left one place value position. Doing this will mean we also add a zero to the number as a zero place-holder.
We do the opposite for division, so when we divide by 10, we move each of the digits one place value to the right, just like this example.\begin{aligned} 230 \times 10 &= 2300 \\ 2300 \div 10 &= 230 \end{aligned}
Powers of 10
Examples
Example 2
Fill in the boxes with the missing numbers.
8 \times ⬚ =800
8 \times ⬚ =80
We can use place a value table to find the power of 10 being multiplied.
Large powers of 10
Examples
Example 3
Solve 13\,000 \div 100.
When we are multiplying our number by a power of 10, it's the same as moving each of the digits to the left in a place value table. Doing this will mean we also add zeros to the number as place-holders.
We do the opposite for division, so when we divide by a power of 10, we move each of the digits to the right in a place value table.\begin{aligned} 230 \times 100 &= 23\,000 \\ 2300 \div 100 &= 23 \end{aligned}