How to Convert Between Fractions and Decimals Effortlessly
By now, you must have spent hours after completing sums on division. Therefore, you must know that division involves the breaking up of a whole into several parts. For example, consider that you have a whole pizza before you, and you divide it into four pieces.
So, how are you going to express this situation mathematically? The answer is easy. However, for that, you will have to know what fraction and decimal stand for.
What is a Fraction?
A fraction refers to the mathematical representation of equal parts of a whole object. As you have seen in the previous example, you have divided the pizza into four equal parts. In that case, the fractional equation for each slice is:
\[\frac{1}{4}\]
Had you divided into two equal pieces, the fraction would stand as \[\frac{1}{2}\].
Moreover, 1 refers to the numerator. It indicates the number of equal parts of the whole. On the other hand, 4 and 2 imply the denominator – the total number of equal parts in the whole collection.
A Quick Sum: 7 out of 10 people ate hamburgers at a party. What is the fraction?
Notably, you also must know about the types of fractions to understand more about changing fractions into decimals.
Take a look at the following table to learn about the types of fractions:
What are the Types of Fractions?
In the subsequent sections, you will learn about converting fractions into decimals. However, first you must know what a decimal is.
What is a Decimal?
Decimal stands for a mathematical expression which show whole numbers and fractional numbers as separate entities. For instance, consider a decimal number 11.6. In this case, 11 refers to the whole number, and 0.6 implies the decimal.
So, how do you arrive at a number like that? Look closely:
1.6 stand for 6 parts of a collection of 10 parts. Therefore, \[\frac{6}{10}\] ultimately leads to .6.
A Quick Sum: Convert 3 parts of 10 whole parts into decimal.
Now that you know what a decimal is, keep an eye on how to convert a fraction to decimal.
What is the Process to Convert a Fraction into a Decimal?
To understand the process to convert fractional numbers to decimal, consider the following steps –
Suppose a proper fraction is \[\frac{5}{8}\], where you will have to divide the numerator 5 with the denominator 8.
Therefore, 8)5 (0.625
- 0
---------------
50
- 48
----------------
20
- 16
----------------
40
- 40
----------------
0
------------------
Consequently, you have come to know about the first step of conversion involving fraction and decimals.
However, you might also run into fractions that put forward recurring decimals. In this particular case, the remainder keeps on repeating itself and never comes down to a 0. For instance, consider the following –
\[\frac{4}{9}\] = 4 ÷ 9.
9)4(0.4444
- 0
---------------------
40
- 36
---------------------
40
- 36
----------------
4
-----------------
This is an example of fraction to decimal where the conversion of this specific fraction leads to the formation of a recurring decimal.
A Quick Sum: Convert \[\frac{7}{11}\] into a decimal and determine whether it is recurring or non-recurring.
Furthermore, the process to turn a mixed number into decimal is the same. Take into account the following example –
The fraction is \[7\frac{1}{4}\]. Convert it into an improper fraction = \[\frac{(7\times 4) + 1}{4} = \frac{29}{4}\].
The process of converting mixed numbers into decimals is –
4)29(7.25
-28
---------
10
- 8
----------
20
-20
----------
0
---------
Therefore, the decimal expression of the mixed fraction \[7\frac{1}{4}\] is 7.25. Now, it is the time for converting decimals into fractions.
How to Convert Decimal to Fraction?
The process for changing decimals to fractions is quite simple. To understand this, you will have to consider two examples.
Example A is a decimal 0.9, and example B is a decimal 0.75. For a decimal, you will always have to assume the denominator to be 1.
Therefore, A = \[\frac{0.9}{1}\] and B = \[\frac{0.75}{1}\]. Since A and B have a decimal point before one and two digits respectively, you will have to multiply both the numerator and denominator of A with 10 and B with 100.
As a result, A = \[\frac{0.9\times 10}{1\times 10}\] and B = \[\frac{0.75\times 10}{1\times 10}\].
Thus, A becomes \[\frac{9}{10}\] and B becomes \[\frac{75}{100}\]. However, A cannot be simplified any further because 9 is not divisible by 10. On the other hand, you can simplify B into \[\frac{3}{4}\]. Therefore, this concludes the process for writing decimals as fractions.
On top of that, there is another process that can help you convert recurring decimals into fractions. For instance, consider a recurring decimal 0.77. You can also write it as the following equation –
Suppose x = 0.77.
Multiply both sides with 10. Therefore, the equation becomes 10x = 7.77.
Now you will have to subtract x from both sides. The equation thus becomes 9x = 7.
Therefore, x = \[\frac{7}{9}\].
Thus, the method for turning recurring decimals into fractions becomes quite easy when you consider recurring decimals as x.
Now you know what fraction and decimals are and how to convert one into the other. However, for further interesting insights into this topic, keep an eye on Vedantu’s website. You can also download our Vedantu app for easier access.
FAQs on Fractions and Decimals Simplified for Students
1. What is a fraction and what are its main parts?
A fraction is a number that represents a part of a whole. It is written as one number over another, separated by a line. The two main parts are:
- The numerator (the top number), which shows how many parts you have.
- The denominator (the bottom number), which shows the total number of equal parts the whole is divided into.
2. What is a decimal and how does it relate to a fraction?
A decimal is another way to write a fraction. It uses a decimal point (.) to separate the whole number part from the fractional part. The digits to the right of the decimal point represent parts of a whole, based on powers of ten (tenths, hundredths, thousandths, etc.). For example, the decimal 0.5 is the same as the fraction 1/2.
3. How do you convert a fraction into a decimal?
To convert a fraction to a decimal, you simply divide the numerator by the denominator. For example, to convert the fraction 3/4 into a decimal, you perform the division 3 ÷ 4, which gives you 0.75. This method works for all types of fractions.
4. What is the method to convert a decimal into a fraction?
To convert a decimal into a fraction, follow these steps:
- Write the decimal as the numerator without the decimal point.
- The denominator will be a power of 10 (like 10, 100, 1000) with the same number of zeros as there are decimal places in the original number.
- Finally, simplify the fraction to its lowest terms.
5. What is the difference between proper, improper, and mixed fractions?
The main difference lies in the value of the numerator compared to the denominator:
- A Proper Fraction has a numerator that is smaller than its denominator (e.g., 2/5). Its value is always less than 1.
- An Improper Fraction has a numerator that is greater than or equal to its denominator (e.g., 7/4). Its value is 1 or more.
- A Mixed Fraction is a combination of a whole number and a proper fraction (e.g., 1 3/4). It is another way to write an improper fraction.
6. Why is it important to find a common denominator before adding or subtracting fractions?
Finding a common denominator is crucial because you can only add or subtract things that are of the same kind or size. The denominator tells you the size of the fractional parts. By converting fractions to have a common denominator, you are ensuring that all the 'pieces' you are combining or taking away are of the same size, making the calculation meaningful. It's like trying to add apples and oranges; first, you must find a common unit, which in fractions is the common denominator.
7. When is it more practical to use fractions instead of decimals in real life?
Fractions are often more practical and intuitive in everyday situations that involve dividing things into equal parts. Common examples include:
- Cooking and Recipes: Measurements like 'half a cup of sugar' (1/2) or 'a quarter teaspoon of salt' (1/4) are standard.
- Telling Time: We often say 'quarter past three' (1/4) or 'half past six' (1/2).
- Measurements: In crafts or construction, measurements like 'three-quarters of an inch' (3/4 inch) are common.
8. Does multiplying fractions always result in a bigger number?
No, this is a common misconception. When you multiply a number by a proper fraction (a fraction with a value less than 1), the result is actually smaller than the original number. This is because you are finding a 'part of' that number. For example, 10 x 1/2 = 5, and 5 is smaller than 10. Multiplication only results in a bigger number when you multiply by a value greater than 1.
9. How do you multiply two decimal numbers?
To multiply two decimal numbers, as per the CBSE Class 7 syllabus for the 2025-26 session, you can follow these steps:
- First, multiply the numbers as if they were whole numbers, ignoring the decimal points.
- Next, count the total number of digits after the decimal point in both of the original numbers.
- Finally, place the decimal point in your answer so that it has the same number of decimal places you counted in the previous step.
10. Can you explain the concept of a recurring decimal with an example?
A recurring decimal, also known as a repeating decimal, is a decimal number where one or more digits repeat forever. This occurs when converting a fraction to a decimal if the division process never results in a remainder of zero. For example, when you convert the fraction 1/3 to a decimal by dividing 1 by 3, the result is 0.3333..., where the digit '3' repeats infinitely. This is written as 0.3 with a bar or a dot over the 3.
