Dividing decimals

Dividing decimals by whole numbers

Dividing decimals by whole numbers works the same way as dividing whole numbers except, just like addition and subtraction of decimals, the decimal point must be kept in line.

Example

Work out 4.14 \div 3.

Example of long division (4.14 / 3)

4.14 \div 3 = 1.38

Dividing numbers by decimals

Equivalent fractions can be used to divide numbers by decimals.

For example, 4 \div 0.2 is the same as \frac{4}{0.2}.

  1. First, note that 0.2 has one decimal place, so multiply the numerator and denominator by 10 to get a whole number. This gives: \frac{40}{2} (which is equivalent to \frac{4}{0.2})
  2. Next, work out 40 \div 2.

40 \div 2 = 20, so 4 \div 0.2 must also equal 20.

Question

Work out 18.9 \div 0.09.

Using equivalent fractions

18.9 \div 0.09 is the same as \frac{18.9}{0.09}.

  1. Note that 0.09 has two decimal places, so multiply the denominator by 100 to get a whole number. Multiply the numerator by 100 as well in order to make an equivalent fraction. This gives \frac{1,890}{9}.
  2. Next work out 1,890 \div 9.

1,890 \div 9 = 18.9 \div 0.09 = 210

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