Page 34 - Mathematics Coursebook

3.2 Multiplying and dividing by 10, 100 and 1000

3.2 Multiplying and dividing by 10, 100 and 1000

When you multiply a whole number or a decimal number by 10, the number becomes ten times bigger.

!is means that all the digits in the number move one place to the left in the place-value table.
24 × 10 = 240

Hundreds Tens Units • Tenths Hundredths An empty space before the
2 4 s decimal point must be fi lled with
a zero.
2 4 0 s

0.24 × 10 = 2.4

Hundreds Tens Units • Tenths Hundredths An empty space at the end of the

0 s 2 4 number, after the decimal point, does
not need to be fi lled with a zero.
2 s 4

When you multiply by 100 all the digits move two places to the le$.
When you multiply by 1000 all the digits move three places to the le$.

Worked example 3.2A

Work out the answer to each of the following.
a 45 × 100 b 3.79 × 10

Solution
Thousands Hundredths Tenths Units • Tenths

4 5 s
4 5 0 0 s

a 45 × 100 = 4500 Move the digits two places to the left and fi ll the empty spaces with zeros.
b 3.79 × 10 = 37.9 Move the digits one place to the left. There are no empty spaces to fi ll with zeros.

Similarly, when you divide a whole number or a decimal number by 10 all the digits in the number
move one place to the right in the place-value table.

24 ÷ 10 = 2.4 Tens Units • Tenths Hundredths

An empty space before the fi rst digit 2 4 s
does not need to be fi lled with a zero.
2 s 4
0.24 ÷ 10 = 0.024
Tens Units • Tenths Hundredths Thousandths
An empty space before the decimal 0 s 2 4
point should be fi lled with a zero.
0 s 0 2 4
When you divide by 100 all the digits move two places to the right.
When you divide by 1000 all the digits move three places to the right.

3 Place value, ordering and rounding 33