What is 7/8 as a decimal?

Solution

Work out the fraction $$\frac78$$ using the following methods to write it as a decimal.

• a) With Long Division- b) Without Long Division

With Long Division

The long division method is very simple. All the fractions can be written as a division expression.

$$\frac78=7\div8$$

The numerator is divided by the denominator to get the decimal value of a fraction. Here 7 is the numerator and 8 is the denominator.

To make 7 divisible by 8, add 0 to 7 to make it 70. Remember to place a decimal point in the quotient when this is done.

As we get the remainder 0 in the third step, we cannot divide further.

The answer is 0.875.

Without long division

The rule to directly convert a fraction to a decimal is

• The denominator should be a number with 1 followed by one or more zeros. Or the denominator should be a number that can be multiplied by a suitable number to make it 10, 100, 1000 etc.- The number of zeros in the denominator is the number of digits the decimal point has to be shifted to the left in the numerator.

Here we have 8 in the denominator, to which 125 can be multiplied to get 1000. The same value should be multiplied by the numerator also as given below.

$$\frac{\mathbf7\boldsymbol\times\mathbf{125}}{\mathbf8\boldsymbol\times\mathbf{125}}\boldsymbol=\frac{\mathbf{875}}{\mathbf{1000}}\boldsymbol=\mathbf0\boldsymbol.\mathbf{875}$$

Remember

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