Converting a Fraction With a Denominator of 10 or 100 to a Decimal

We should recall decimal place value charts. We know that, to the right of a decimal, the places values are the tenths, hundredths, thousandths and so on.

The rule says that the decimal point in the numerator shifts to the left as many places as the number of zeros after 1 in the denominator.

Consider here, fractions with denominators of 10 or 100

Rules to convert a fraction with a denominator of 10 to a decimal

• Suppose we have a fraction $\frac{7}{10}$.

• At first, we write the numerator 7 only.

• Then we look at the denominator which is a ten which corresponds to the decimal place value tenth. So, 7 has a place value of a tenth. For this we put a decimal point before 7. So, $\frac{7}{10}$ becomes the decimal .7 or 0.7

• Alternately, as the number of zeros in a 10 is 1, the decimal shifts one place to the left in 7 to make it 0.7

Rules to convert a fraction with a denominator of 100 to a decimal

• Next consider a fraction $\frac{97}{100}$.

• At first, we write the numerator 97 only.

• As we were dividing with a 100, we are looking at a place value of a hundredth. The digit 7 has a place value of a hundredth. So, a decimal point is put before 9 and we get $\frac{97}{100} = .97$ or $0.97$.

• Alternately, as the number of zeros in a 100 is 2, the decimal point shifts two places to the left in 97 to make it 0.97

Write $\frac{6}{10}$ as a Decimal.

Solution

Step 1:

At first, we only write the numerator 6 as 6.0

Step 2:

Since the denominator 10 has a single zero, we shift the decimal point in 6.0 one place to the left and get .6 or 0.6 as the answer.

Step 3:

So, $\frac{6}{10} = 0.6$

Write $\frac{48}{100}$ as a decimal.

Solution

Step 1:

At first, we write the numerator 48 as a decimal 48.0.

Step 2:

Since the denominator 100 has two zeros, we shift the decimal point in 48.0 two places to the left, and get the answer as .48 or 0.48

Step 3:

So, $\frac{48}{100} = 0.48$