Last updated on July 5th, 2025
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.
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.
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
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.
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 |
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…
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 |
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.
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.
Convert 3/5 into a decimal.
3/5 = 0.6
Divide the numerator (3) by the denominator (5): 3 5 = 0.6.
Convert 0.75 into a fraction.
0.75 = 3/4
Write 0.75 as 75/100 and simplify, dividing both numerator and denominator by 25.
Convert 7/8 into a decimal.
7/8 = 0.875
Divide 7 by 8 using long division to get 0.875.
Write 0.6 as a fraction in its simplest form.
3/5
The decimal 0.6 means 6/10. Simplifying 6/10 by dividing both the numerator and denominator by 2, we get 3/5.
What is the fraction equivalent of the repeating decimal 0.3?
1/3
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.
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.
: She loves to read number jokes and games.