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Last updated on July 5th, 2025

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Relationship Between Fractions and Decimals

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Fractions and decimals represent the same numerical value differently. Fractions are a type of mathematical expression and are often represented in the p/q form. In this form, p and q are whole numbers, and q 0. Fractions can be converted to a decimal form by using the long division method or by converting the denominator into a power of 10.

Relationship Between Fractions and Decimals for Australian Students
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What is Fractions-to-Decimal Conversion?

The process of converting a fraction to its equivalent decimal form is called fraction-to-decimal conversion. Understanding this process helps in solving problems more efficiently.
 

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How to Convert Fractions to Decimals?

We can use two methods to convert a fraction into its decimal form. They are called long division and multiples of 10 methods.
 

Long Division Method

In this method, we divide the numerator by the denominator.

Step 1: The numerator becomes the dividend, and the divisor is the denominator. 
        
Step 2: Compare the values of the numerator and the denominator. If the numerator is less than the denominator, then add a decimal point to the quotient and place a zero next to the dividend. 

Step 3: Follow the process involved in the long division method. Bring down zeros if necessary and continue until the remainder becomes zero. We can also stop the division if we notice a repeating pattern.

Example: Convert 5/6 to a decimal.

5 ÷ 6 = 0.833… (repeating)

So, 5/6 = 0.83

 

Multiples of 10 Method

Adjust the denominator to a power of 10 (such as 10, 100, or 1000) and then rewrite the fraction as a decimal. 

Step 1: Choose a number to multiply both the numerator and denominator so that the denominator becomes a power of 10 (10, 100, 1000, etc.). 

Step 2: Apply the same multiplier to the numerator and denominator.

Step 3: Once the denominator is a power of 10, write the fraction in decimal form. 
 

Example: Convert 2/5 to a decimal.

Multiply numerator and denominator by 2: 2 x 2 / 5 x 2 = 410

Decimal form: 0.4

So, the answer is 0.4

Professor Greenline from BrightChamps

How to Convert Decimals to Fractions?

Every decimal number can be written as a fraction. By removing the decimal point and dividing by a power of 10, we can convert any decimal into its fractional form and simplify it. 
 

Step 1: Write the number without the decimal point. 

Step 2: Place the number over 10, 100, or 1000, depending on the number of decimal places.

Step 3: Reduce the fraction to its simplest form. 
 

Example: Convert 7.2 to a fraction.

Writing the number without the decimal point, we get 72 

Divide by 10: 72/10

To simplify, 72/10, we should find the GCF of 72 and 10. 

So let’s list the factors of 72 and 10.

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 10: 1, 2, 5, 10

Among the factors of 72 and 10, the greatest common factor (GCF) is 2.
Now, we should divide the numerator and denominator by the GCF

72 ÷ 2 / 10 ÷ 2 = 36/5


So, 72/10 it can be simplified to 36/5

Therefore, the fraction form of 7.2 is 36/5. 
 

Professor Greenline from BrightChamps

Fraction-to-decimal Chart

A fraction-to-decimal chart makes conversion easy by showing common fractions with their decimal equivalents. Always remember that proper fractions have a numerator smaller than the denominator and improper fractions have a numerator equal to or greater than the denominator, so their decimal values are 1 or more.

 

Let’s list some common fractions and their decimal forms in a chart. 

 

Fraction Decimal
1/2 0.5
1/3 0.3 = 0.333...
1/4 0.25
1/5 0.2
1/6 0.16
1/8 0.125
1/10 0.1
1/100 0.01
3/7 0.428571
3/2 1.5
3/4 0.75
4/3 1.33

 

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What are the Types of Decimal Fractions?

Decimal fractions are divided into two main types: terminating and non-terminating. The second type can be divided further into non-terminating, repeating, and non-terminating, non-repeating decimals. 
 

Terminating Decimals: As the name suggests, the numbers after the decimal point do not go on forever, as they come to an end.
    
 Example: 0.75, 2.5, 4.125

 

Non-terminating Decimals: Here, the numbers after the decimal point do not end as they continue indefinitely. Non-terminating decimals are further classified into two types:
 

Repeating (recurring) decimals: A specific set of digits repeats in pattern.


Example: 0.333… = 0.3, 

 0.727272… = 0.72
 

Non-repeating decimals: The decimal digits continue without a repeating pattern. These are called irrational numbers.

 

Example:

𝜋 = 3.141592653…, 

2 = 1.414213…

Professor Greenline from BrightChamps

Operations on Decimal Fractions

We can perform different mathematical operations on decimal fractions, including addition, subtraction, multiplication, and division. The following table explains these operations in detail.
 

Operation Description Example Result
Addition Align the decimal points and add as usual 3.6 + 2.45 6.05
Subtraction Align the decimal pointd and subtract normally 7.8 - 3.25 4.55
Multiplication

Multiply like whole numbers, then place the decimal in the product based on the total number of decimal places in the factors.

1.2 x 3.5 4.2
Division Divide normally and adjust the decimal point accordingly. 8.4 ÷ 2 4.2
Coversion to Fraction Write the decimal over a power of 10 and simplify 0.6/10 3/5

 

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Common Mistakes of Relationship Between Fractions and Decimals and How to Avoid Them

Understanding the relationship between fractions and decimals is important, but students often make common mistakes while converting or performing operations. Here are some frequent errors and tips on how to avoid them.

Mistake 1

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Assuming a larger denominator means a larger decimal value
     

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We should remember that a larger denominator will actually lower the value of the fraction. (e.g., 12 = 0.5 but 1/10 = 0.1). 

Mistake 2

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Forgetting to align decimal points when adding or subtracting decimals 
 

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 Before adding or subtracting decimals, we should make sure to line up the decimal points so that they are aligned.

Mistake 3

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Not placing the decimal point correctly after multiplying decimals

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While multiplying decimal numbers, it is always advisable to ignore the decimal points for both multiplier and multiplicand. For example, when we multiply 1.5 and 1.2345, the answer is 1.85175. Here, 1.5 has 1 decimal place and 1.2345 has 4 decimal places. Hence, the answer should have 5 decimal places.

Mistake 4

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 Ignoring repeating decimals when converting them to fractions

 

 

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Recognize patterns in repeating decimals (e.g., 0.3 = 1/3) and use algebraic methods to convert them.

Mistake 5

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Misplacing the decimal when dividing by 10, 100, or 1000 
 

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 Move the decimal left for division (e.g., 45.6  10 = 4.56) and right for multiplication.

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Professor Greenline from BrightChamps

Real-life Applications of Relationship Between Fractions and Decimals

Fractions and decimals are used in many everyday activities, from handling money to measuring ingredients and distances. Here are three common real-life applications where understanding their relationship is important.
 

  • Money and Finance: Prices, discounts, and taxes often involve decimals and fractions. For example, if an item costs $4.50, it can be written as 9/2 in fraction form. 
     
  • Cooking and Baking: Recipes use fractions (e.g., 1/2 cup of sugars) and sometimes require conversions to decimals for accurate measurements.
     
  • Measurement and Construction: Lengths and distances are often given in fractions (e.g., 3/4 inch) but may need to be converted into decimals for precision tools.
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Solved Examples for Relationship Between Fractions and Decimals

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Problem 1

Convert 3/5 into a decimal.

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3/5 = 0.6

Explanation

 Divide the numerator (3) by the denominator (5): 3  5 = 0.6.
 

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Problem 2

Convert 0.75 into a fraction.

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0.75 = 3/4

Explanation

Write 0.75 as 75/100 and simplify, dividing both numerator and denominator by 25.

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Problem 3

Convert 7/8 into a decimal.

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7/8 = 0.875

Explanation

 Divide 7 by 8 using long division to get 0.875.

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Problem 4

Write 0.6 as a fraction in its simplest form.

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3/5

Explanation

 The decimal 0.6 means 6/10. Simplifying 6/10 by dividing both the numerator and denominator by 2, we get 3/5.
 

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Problem 5

What is the fraction equivalent of the repeating decimal 0.3?

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1/3

Explanation

Let x = 0.3. Multiplying both sides by 10 gives 10x = 3.3. Subtracting the original equation from this new equation, 10x – x = 3.3 – 0.3, gives 9x = 3. Solving for x, we get x = 3/9 = 1/3.
 

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Fun Fact

: She loves to read number jokes and games.

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