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

Introduction

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 5910059100.
• 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 59100=.5959100=.59 or 0.590.59
• 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 865100865100.
• 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 8651000=.8658651000=.865 or 0.8650.865
• 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

Example 1

Write 3610036100 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, 36100=0.3636100=0.36Example 2

Write 23710002371000 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, 2371000=0.237