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Last updated on July 4th, 2025

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Decimal Fraction

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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.

Decimal Fraction for Australian Students
Professor Greenline from BrightChamps

What is a Decimal Fraction?

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.).

Professor Greenline from BrightChamps

How to Read Decimal Fractions?

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”.

Professor Greenline from BrightChamps

What are the Operations on Decimal Fraction?

Basic mathematical operations are applicable on decimal fractions. All these operations are discussed in detail:

 

 

Addition of Decimal Fractions 

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, 

  • 45/100 = 0.45
  • 65/1000 = 0.065
     

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


 

Subtraction of Decimal Fractions

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.

 

 

Multiplication of Decimal Fractions

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.

 

Division of Decimal Fractions

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. 
 

Professor Greenline from BrightChamps

What Are the Types of Decimal Fraction?

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:
 

  • Terminating Decimals
  • Non-terminating Repeating Decimals
  • Non-terminating Non-repeating Decimals
     

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. 
 

Professor Greenline from BrightChamps

Conversion to Decimal Fractions

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:
 

  • Converting Fractions to Decimal Fractions

    Let’s take the example of the fraction 5/4.

    Step 1: First, find a number that, when multiplied by the denominator, results in 10 or a multiple of 10. 

    Step 2: In this case, multiplying 4 by 25 gives 100.

    Step 3: Multiply with the same number to the numerator and denominator.
     

        (5 x 25) / (4 x 25)  = 125/100

Thus, the decimal fraction of 5/4 is 125/100 or 1.25 

 

  • Converting Mixed Numbers to Decimal Fractions

    Let’s take an example of 2 x (1/5)

    Step 1: First, we need to convert the mixed number, 2 (1/5) into an improper fraction.

    2 x (1/5) = 11/5

    Step 2: Next, to get a denominator of 10, we must multiply both the numerator and denominator by 2.

    (11 x 2)/ (5 x 2) = (22/10)

    Therefore, the decimal fraction of 2 x (1/5) is  22/10.  

 

  • Converting Decimal Numbers to Decimal Fractions

    Let’s take an example of 6.2

    Step 1: Write the decimal number as a fraction with 1 in the denominator.

    6.2/1

    Step 2: Shift the decimal one place to the right and add a zero to the denominator.
    62.0/10

    Step 3: Now that the numerator is a whole number, we get the decimal fraction.

    6.2 = 62/10

    Thus, 6.2 as a decimal fraction is 62/10.
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Common Mistakes of Decimal Fraction

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. 

Mistake 1

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 Ignoring Place Values in Multiplication and Division
 

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Treating decimal numbers like whole numbers in multiplication and division. For example, 0.2 × 0.3 = 0.6 (wrong) instead of 0.06. Count how many decimal places there are in both numbers, and then check that the answer has the same total number of decimal places.

 

For example, 0.2 × 0.3 (both the numbers have 1 decimal place)
 0.2 ×0.3 = 0.06 (the answer has 2 decimal places in total). 
 

Mistake 2

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Forgetting to Align Decimal Points in Addition and Subtraction

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 Properly align the decimal points when performing the addition or subtraction of decimal numbers. Keep in mind to arrange the numbers in the correct columns, and if needed, add zeros to the numbers that have fewer decimal places.

For example, add 3.2 + 45.67

Rather than aligning like:
     3.2 
+ 45.67

Add a zero to 3.2:
     3.20 
+ 45.67
    
 

Mistake 3

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Incorrectly Converting Decimals to Fractions

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Writing decimals as fractions without considering place value. For example, 0.25 = 25/1000 (wrong) instead of 25/100. Always identify the place value of the last digit. 

Treating Repeating Decimals as Terminating

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Treating Repeating Decimals as Terminating

 

 

 

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Students mistakenly assume that 0.333… ends at 0.3 and they are rounding it too early. For instance, 1  3 = 0.3, which is wrong. 
The correct answer is 0.333 or 0.3. Always use the bar notation for the repeating decimals (e.g., 0.3.) and don’t round unless the question requires it. 
 

Mistake 5

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 Misplacing the Decimal Point
      

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 Always remember to place the decimal point in the correct place when dividing and multiplying by powers of 10. For example, students mistakenly write 3.45 × 10 = 3.450. 
The correct answer is 34.5. The decimal point moves to the left while dividing and to the right while multiplying by 10 respectively.

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Professor Greenline from BrightChamps

Real Life Applications of Decimal Fraction

Decimal fraction is easy for calculation, just by shifting the decimal point, it ensures the precision and correctness of the number.

 

  • Money and Finance: Prices, bills, and bank transactions involve decimals (e.g., $4.75, $99.99). Calculating discounts, interest rates, and taxes require decimal fractions. 
     
  • Measurements in Daily Life: Length, weight, and volume are often measured in decimals (e.g., 2.5 kg, 1.75 liters). Cooking recipes use decimals for precise ingredient amounts. 
     
  • Science and Medicine: Medication doses are measured in decimals (e.g., 2.5 mg of medicine). Scientific measurements use decimals for accuracy (e.g., temperature: 36.7° C).  
     
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Solved Examples for Decimal Fraction

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Max, the Girl Character from BrightChamps

Problem 1

Convert 0.75 into a fraction.

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0.75 = 3/4.
 

Explanation

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

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

Add 2.5 + 0.75 + 3.125.

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6.375

Explanation

 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
 

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Max, the Girl Character from BrightChamps

Problem 3

Multiply 4.6 × 3

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13.8

Explanation

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
 

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Max, the Girl Character from BrightChamps

Problem 4

Write 0.75 as a fraction in its simplest form.

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 0.75 = ¾

 

Explanation

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 

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Max, the Girl Character from BrightChamps

Problem 5

Divide 6.4 by 0.8.

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 6.4 ÷  0.8 = 8

Explanation

 Convert 0.8 into a whole number by multiplying both numbers by 10: (6.4 x 10) ÷  (0.8 ÷ 10) = 64 ÷  8 = 8.

 

Max from BrightChamps Praising Clear Math Explanations
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