Session 2: Decimal Fraction – Definition, Types, Conversion, Steps, Interactive and Examples

What is Decimal Fraction?

A decimal fraction is a fraction whose denominator is 10, 100, 1000 and so on. Examples, , etc are all decimal fractions. In this section, we shall define tenths, hundredths, thousandths, etc. and use them to express fractions as decimals. 

Tenths as Decimal

Consider the following figure. It is divided into ten equal parts, and one is shaded. The shaded part represents one-tenth of the figure and is written as \(\frac{1}{10}\). The fraction \(\frac{1}{10}\) is called one-tenth and is also written as 0.1.

1) Express 4 tenths as a decimal.   

The place value to the right of the decimal is called the tenth place because ten-tenths make a whole. 

If we have the fraction \(\frac{4}{10}\), we have four out of the ten pieces required to make a whole. Since the denominator is 10, we can write this as 0.4. The decimal 0.4 means that we have 4 tenths and no wholes. 

4 tenths=\(\frac{4}{10}\)=0.4

Hundredths as Decimal

Consider the figure given below. It is divided into hundred equal parts, and one is shaded. The shaded part represents one-hundredth of the figure and is written as \(\frac{1}{100}\). The fraction 1100 is called one-hundredth and is also written as 0.01.

2) Express 8 hundredths as a decimal. 

The place value to the right of the tenth place is called the hundredths place because a hundred-hundredths make a whole. 

If we have the fraction \(\frac{8}{100}\), we have eight out of a hundred pieces required to make a whole. Since the denominator is 100, we can write this as 0.08. The decimal 0.08 means that we have 8 hundredths and no wholes. 

8 hundredths=\(\frac{8}{100}\)=0.08

Similarly, \(\frac{82}{100}\) can be written as 

=8 tenths 2 hundredths
=0.82

Thus,

• The decimal number for 8 tenths is 0.8. 
• The decimal number for 2 hundredths is 0.02. 
• The decimal number for 8 tenths 2 hundredths or 82 hundredths is 0.82. 

Thousandths as Decimal

Consider the figure given below. It is divided into thousand equal parts, and one is shaded. The shaded part represents one-thousandth of the figure and is written as \(\frac{1}{1000}\). The fraction \(\frac{1}{1000}\) is called one-thousandth and is also written as 0.001.    

3) Express 6 thousandths as a decimal. 

The place value to the right of the hundredth place is called the thousandths place because a thousand-thousandths make a whole. 

If we have the fraction \(\frac{6}{1000}\), we have six out of the 1000 pieces required to make a whole. Since the denominator is 1000, we can write this as 0.006. The decimal 0.006 means that we have 6 thousandths and no wholes. 

6 thousandths=\(\frac{6}{1000}\)=0.006

Similarly, \(\frac{827}{1000}\) can be written as 

=8 tenths 2 hundredths 7 thousandths
=0.827

Thus,

• The decimal number for 8 tenths is 0.8. 
• The decimal number for 2 hundredths is 0.02.
• The decimal number for 7 thousandths is 0.007. 
• The decimal number for 8 tenths 2 hundredths 7 thousandths or 827 thousandths is 0.827.

Decimal to Fraction Conversion

Sometimes we will need to either change a decimal to a fraction or a fraction to a decimal.

Steps to Convert Decimal to Fraction

A decimal can always be converted into a fraction by using the following steps:

Step 1: Obtain the decimal.

Step 2: Take the numerator as the number obtained by removing the decimal point from the given decimal.

Step 3: Identify the value of the last place in the denominator. Use this place to write the decimal.

4) Express the following decimals as fractions in the lowest form:

i. 2.75

ii. 0.008

We have, 

i. 

ii. 

Fraction to Decimal Conversion

At the beginning of this section, we have mentioned that decimals are fractions with denominators 10, 100, 1000, etc. Not all fractions can be changed to decimal form easily.

Steps to Convert Fraction to Decimal

To write fractions that have denominators other than 10, 100, 1000 and so on into decimals, we follow the following steps:

Step 1: Obtain the fraction and convert it into an equivalent fraction with a denominator of 10, 100 or 1000.

Step 2: Then write the equivalent fraction as a decimal.

5) Express the following fractions as decimals:

i. \(\frac{3}{5}\)

ii.\(6\frac{1}{4}\)

We have,

Decimal Fraction – Examples

Example 1

Write each of the following as decimals

i. We have, 

\(\frac{3}{10}\)=3 tenths=0.3

ii. We have, 

\(\frac{2}{100}\)=2 hundredths=0.02

iii. We have, 

\(\frac{18}{1000}\)=18 thousandths=0.018

iv. We have, 

Example 2

Write the following as decimals

i. \(\frac{3}{4}\)

ii. \(6\frac{2}{5}\)

i. Write \(\frac{3}{4}\) with 100 as the denominator

Now, write the fraction as a decimal

ii. Write \(6\frac{2}{5}\)as an improper fraction. 

Write the new fraction with 10 as the denominator

Write the fraction as a decimal

Example 3

Write the following decimals as fractions:

i. 4.16

ii. 1.25

iii. 0.02

iv. 1.005

We have, 

Remember this!

A decimal fraction is a fraction whose denominator is 10, 100, 1000 and so on. Tenth: One part in ten equal parts.  Hundredth: One part in hundred equal parts.  Thousandth: One part in thousand equal parts.