Converting a Fraction With a Denominator of 100 or 1000 to a Decimal

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

In this lesson, we are considering fractions with denominators of 100 or 1000.

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

• Let us consider a fraction $\frac{59}{100}$.

• At first, we write the numerator 59 only.

• As we were dividing with a 100, we are looking at a place value of a hundredth. The digit 9 has a place value of a hundredth. So, a decimal point is put before 5 and we get $\frac{59}{100} = .59$ or $0.59$

• Alternately, as the number of zeros in a 100 is 2, the decimal point shifts two places to the left in 59 to make it 0.59

Rules to convert a fraction with a denominator of 1000 to a decimal

• Let us consider a fraction $\frac{865}{100}$.

• At first, we write the numerator 865 only.

• As we are dividing by 1000, we are looking at a place value of a thousandth. The digit 5 has a place value of a thousandth. So, a decimal point is put before 8 and we get $\frac{865}{1000} = .865$ or $0.865$

• Alternately, as the number of zeros in 1000 is 3, the decimal point shifts three places to the left in 865 to make it 0.865

Write $\frac{36}{100}$ as a decimal.

Solution

Step 1:

At first, we write the numerator 36 as 36.0

Step 2:

Since the denominator 100 has two zeros, we shift the decimal point in 36.0 two places to the left, and get .36 or 0.36 as the answer.

Step 3:

So, $\frac{36}{100} = 0.36$

Write $\frac{237}{1000}$ as a decimal.

Solution

Step 1:

At first, we write the numerator 237 as 237.0

Step 2:

Since the denominator 1000 has three zeros, we shift the decimal point in 237.0 three places to the left, and get .237 or 0.237 as the answer.

Step 3:

So, $\frac{237}{1000} = 0.237$