Decimal Fraction – Definition with Examples

Definition of Decimal Fractions

The prerequisite for understanding decimal fractions is the understanding of normal fractions. You must know that a fraction comprises a numerator (top part) and a denominator (bottom part). The correct way of writing a fraction is –

X is the numerator in this example, and y is the denominator.
Decimal fractions are the fractions in which the denominator (y in the image) must be 10 or a multiple of 10 like 100, 1000, 10000, and so on. The numerator can be any integer (between -infinity and +infinity). These decimal fractions are usually expressed in decimal numbers (numbers with a decimal point).

In algebra, a decimal fraction is a number having 10 or the powers of 10 like 10¹, 10², 10³, and so on in the denominator.

Examples of Decimal Fractions

• 7/10000 is a decimal fraction written in the decimal form as 0.0007.
• 19/10 is a decimal fraction written in the decimal form as 1.9.
• 39/1000 is a decimal fraction written as 0.039.

Non Examples of Decimal Fractions

Other fractions with non-ten numbers in the denominator are not decimal fractions. They are:

• 37/8
• 2/1083
• 83/145

Let us consider a scenario where 1 is in the numerator. We will consider different denominators to understand how these terms are read with this numerator.

• 1/10 is read as one-tenth.
• 1/100 is read as one-hundredth.
• 1/1000 is read as one-thousandth.

When the value of the numerator is more than one, we add an ‘s’ to the name. So, for instance, 3/10 is read as three-tenths.

History of Decimal Fractions

The Chinese first developed and used decimal fractions at the end of the 4th century BC, which spread to the Middle East before reaching Europe.

Conversion to Decimal Fractions

1. Conversion from fractions to decimal fractions

• Let us consider an example of a fraction, 3/2.
• The first step would be to consider the number that gives 10 or a multiple of 10 when multiplied by the denominator. In this case, 5 multiplied by 2 gives 10.
• Now multiply the numerator and denominator with the same number to get your decimal fraction. Here, 3 x 5/ 2 x 5 gives 15/10.
• Thus, the decimal fraction of 3/2 is 15/10.

2. Conversion from mixed numbers to decimal fractions

• Convert the mixed fraction into a normal fraction.
• Follow the steps for converting fractions to decimal fractions.

3. Conversion from decimal numbers to decimal fractions

• Write the original decimal number in the numerator and denominator form by placing 1 in the denominator: 4.3/1.
• For every space that you move the decimal point, add a zero next to the 1 in the denominator: 43/10 (As we can see one shift of decimal space, one 0 must be added to the denominator).

4.3/1

43.0/10

• Once the number in the numerator is non-decimal, you have got your decimal fraction: 4.3 = 43/10.

Real-Life Application of Decimal Fractions

Decimal fractions are used for understanding precise quantities instead of whole numbers. You will also use them for expressing percentages. For instance, 97% can be written as 97/100 for ease of calculation.

Here are some scenarios where you might encounter decimal fractions:

• Coins (They are a fraction of Rupees)
• Weighing products
• Measuring ingredients while cooking

Solved Examples

Example 1

Convert 2 ½ into a decimal fraction.

= 2 ½

= 5/2

= 5 x 5 / 2 x 5

= 25 / 10

Example 2

Convert 5.4 into a decimal fraction.

= 5.4/1

= 54/10

Example 3

Convert 8 ⅕ into a decimal fraction.

= 8 ⅕

= 41/5

= 41 x 2 / 5 x 2

= 82/10

Conclusion
Decimal fractions encourage students to learn about precise quantities. This will help them understand weights like 3.2 kg and distances like 7.85 km. The first step towards a better understanding of decimal numbers is practicing decimal fraction problems every day. The idea of taking a pen and paper to solve sums is dull and uninteresting for students. They need entertaining ways to entice them towards practicing the sums.

SplashLearn makes the process of practicing decimal numbers fun and interactive for kids. With dozens of decimal fraction games, your child will never fall short of options to practice math. Instead, learning becomes engaging with interesting games that allure your kids towards solving sums.

Let’s do it!

Instead of teaching decimal fractions and handing out practice worksheets to your children, ask them to find and make decimal fractions of the decimals or fractions you say.

Practice Problems

1

Convert 6.34 into a decimal fraction.

634/100
634/10
6.34/100
6.34/10
CorrectIncorrect
Since there are two places after the decimal point, the decimal fraction of 6.34 would be 634/100.
2

Convert 4 ½ into a decimal fraction.

4/2
4/10
45/100
45/10
CorrectIncorrect
4 ½ can be written as 4.5 and since there is only one place after the decimal point, it’s decimal fraction would be 45/10.
3

Convert 8/5 into a decimal fraction.

16/10
8/100
160/100
16/100
CorrectIncorrect
Multiplying the numerator and the denominator by 2 we get, 8/5 = 16/10
4

125/10
125/100
25/20
5/4
CorrectIncorrect