Last updated on July 4th, 2025
A decimal fraction’s denominator (the bottom number) is a power of 10, such as 10, 100, or 1,000. We often express them using a decimal point, rather than writing them as fractions. For instance, 2/10, 5/10, and 6/100 can be represented as decimals like 0.2, 0.5, and 0.06. Here, we will discuss decimal fractions and its applications.
A fraction comprises a numerator and a denominator. In a decimal fraction, the fraction has a denominator that is a power of 10. The first thing to remember when we convert a decimal to a fraction is to express the denominator as a power of 10. Also, the number of zeros in the power of 10 should be equal to the number of decimal places in the given number. In short, a decimal fraction will have a denominator of 10 or its powers, like 100, 1000, 10000, and so on.
For example,
0.5 = 5/10
0.25 = 25/100
0.75 = 75/100
These fractions all have denominators that are powers of 10 (10, 100, etc.).
Decimal fractions can be read in two ways: by naming each digit separately after the decimal point or by using place values. Understanding how to read them correctly helps in math and everyday life.
Step 1: Read the whole number (if any) before the decimal point. For example, 3.125
Step 2: Say the word “point” when you reach the decimal (.).
Step 3: Read each digit, one by one, after the decimal point separately. For example, 3.125 can be read as “three point one two five”.
Step 4: You can also read the decimal as a fraction by using place values. For example, 3.125 as “three and one hundred twenty-five thousandths”.
Basic mathematical operations are applicable on decimal fractions. All these operations are discussed in detail:
The addition of decimal fractions can be done in two ways.
Convert decimal fractions to decimal form before adding.
Step 1: First, convert them into decimal form.
For example, if we need to add 45/100 and 65/1000,
Step 2: Now, adding them together:
0.45 + 0.065 = 0.515
Step 3: To make it back to a fraction, look for how many decimal places are there.
Here, there are three digits after the decimal point. So we use 1000 as the denominator. To convert 0.515 into a fraction, we need to multiply and divide it by 1000. 0.5151000 1000 = 515/1000
So the answer is 515/1000
Convert the given decimal fractions to like fractions before adding.
Step 1: First, make both the fractions into like fractions.
For example, 45/100 and 65/1000
For that, find the LCM of both denominators, 100 and 1000.
The LCM is 1000
Step 2: Convert each fraction
45100 = 45 10100 10 = 4501000
651000 already has a denominator of 1000, so it remains the same.
Step 3: Add them together
4501000 + 651000 = 5151000
So the answer is 515/1000
Similarly, to subtract decimal fractions, convert them into decimal form first. For example, if we subtract 65/1000 from 45/100.
45100 = 0.45
651000 = 0.065
Now, subtracting
0.45 – 0.065 = 0.385
Convert back into fraction,
0.3851000 × 1000 = 3851000
So the answer is 385/1000.
While multiplying a decimal fraction by a power of 10, it is all about calculating the place of the decimal point as per the number of zeros in the power of 10. For example, 63.457 × 100 = 6345.7, here, the power of 10 is 102. We multiply it by 63.457, we count the number of zeros and shift the decimal point two places accordingly.
When we divide a decimal fraction by 10 or any power of 10, we move the decimal point to the left. We change the number of places by counting how many zeros there are in the power of 10 we divide.
For example, 63.457 100 = 0.63457
(since the denominator 100 (102) has two zeros, we move the decimal two places to the left.
A number can be written as a decimal with a finite number of decimal places or a decimal with an infinite number of decimal places. Decimals can be classified into three types:
A decimal fraction can be represented as a decimal with a finite number of decimal places. The number of zeros in the power of 10 in the denominator determines the number of decimal places. Hence, decimal fractions can be considered as terminating decimals, but not all terminating decimals are decimal fractions unless their denominator can be expressed as a power of 10.
To convert numbers into decimal fractions, different methods are used depending on whether the number is a fraction or a decimal or a mixed fraction. The methods are discussed below:
(5 x 25) / (4 x 25) = 125/100
Thus, the decimal fraction of 5/4 is 125/100 or 1.25
To solve mathematical problems easily, understanding the concept of decimal fractions is important and helpful. However, students often make some mistakes when they work with these types of numbers. Recognizing these errors and their helpful solutions will help students improve their mathematical knowledge.
Decimal fraction is easy for calculation, just by shifting the decimal point, it ensures the precision and correctness of the number.
Convert 0.75 into a fraction.
0.75 = 3/4.
0.75 has two decimal places, meaning it is over 100
75/100
Simplify by dividing both numerator and denominator by 25
(75 ÷ 25) / (100 ÷ 25) = 3/4
Add 2.5 + 0.75 + 3.125.
6.375
Align the numbers by the decimal point
2.500
+0.750
+3.125
--------
6.375
Add digit by digit, just like whole numbers, while keeping the decimal point in place
Multiply 4.6 × 3
13.8
To begin with, ignore the decimal point and multiply it as whole numbers:
46 × 3 = 138.
Since 4.6 has one decimal place, place one decimal place in the result.
So, 4.6 × 3 = 13.8
Write 0.75 as a fraction in its simplest form.
0.75 = ¾
Here, we need to find the simplest form of 0.75.
It can be written as 0.75 = 75/100
Next, simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
The GCF of 75 and 100 is 25.
75 ÷ 25 = 3
100 ÷ 25 = 4
Hence, 0.75 = 3/4
Divide 6.4 by 0.8.
6.4 ÷ 0.8 = 8
Convert 0.8 into a whole number by multiplying both numbers by 10: (6.4 x 10) ÷ (0.8 ÷ 10) = 64 ÷ 8 = 8.