How to divide decimals

• When dividing decimals by powers of 10, it is useful to have a good knowledge of place value.

• The short division method of multiplication can be used to divide a decimal by a whole number.

• Equivalent fractions can be used to divide decimals.

It may be useful to review place value.

When dividing decimals by powers of 10, a good understanding of place value is needed.

• The order of place value of digits in a number from right to left is: units, tens, hundreds, thousands, ten thousands, hundred thousands, etc.

• Units are often referred to as ones.

To divide decimals by powers of ten using place value labels:

• Write the digits of the decimal using place value labels.

• Start with the first non-zero digit.

  • To divide by 10 move each digit one place to the right.

  • To divide by 100 move each digit two places to the right.

  • To divide by 1000 move each digit three places to the right.

  • If the answer is less than one, write a zero to show zero units. Fill any empty columns after the decimal point with zeros. This ensures each digit has the correct value.

The process can also be completed without place value labels.

Short division is used to divide a decimal by a single-digit whole number:

• Set out the division. Write the question in bus stop form.

  • The divisor goes outside the bus stop.

  • The dividend goes inside the bus stop.

  • The quotient will be written on the top of the bus stop.

• Write the decimal point in the quotient answer space directly above the decimal point of the dividend.

• Starting with the first digit, divide each digit of the dividend by the divisor. Write the answers above the line.

• If there is a remainder when dividing a digit, carry the remainder to the next digit.

It may be helpful to review short division first.

To divide two decimals using equivalent fractions and short division:

• Write the division as a fraction. The numerator is the dividend and the denominator is the divisor.

• Make the divisor a whole number by rewriting the fraction as an equivalent fraction with a whole number denominator:

  • Multiply the denominator by the appropriate power of ten.

  • Multiply the numerator by the same power of ten.

• Set out the division in bus stop form. The divisor (numerator) is outside the bus stop and the dividend (the denominator) is inside the bus stop. Write the decimal point in the quotient answer space directly above the decimal point of the dividend (if there is one).

• Process the division.

It may be helpful to review short division first.

Practise dividing decimals in this quiz. You might need a pen and paper to help with your workings out.

In decimal measurements, conversions between measurements can involve division by 10, 100 and 1000.

A joiner given a length in millimetres will convert to centimetres by dividing by 10.

To convert a length in millimetres to metres it will be a division by 1000.

A dressmaker uses 0∙4 metres of ribbon to make a rosette. Ribbon comes in 2∙5 metre lengths on a spool.

To work out how many rosettes can be made from one spool of ribbon, the calculation is 2∙5 divided by 0∙4.