Fraction to Decimal

The fraction to decimal conversion can be defined as the process of converting a number represented in form of p/q, where p and q belong to whole numbers and q is not equal to 0 into a decimal form by either converting the denominator to a power of 10 or by long division method. Let us learn different ways of converting fractions to decimals in this article.

Any number which is represented in a fraction form is divided into two parts i.e., numerator and denominator. Generally, to convert a number from fraction to decimal form we divide the numerator by the denominator. Fractions are represented in the form of p/q, where q≠0. While the decimal numbers are formed by connecting the whole number part and fractional part through a decimal point, for example, 7.575. Let us explore some more illustrations to understand the fraction to decimal conversion in detail.

Fraction to Decimal Conversion

Here is a real-life example to understand fraction to decimal conversion. Emma divides her cardboard into 12 equal parts. She painted the flowers of different colors on each part of the cardboard. Amongst the 12 slots, she reserved 5 equal portions for red color flowers, 3 portions for green color flowers, and 4 for orange color flowers. Let us write the portion given to flowers of each color in a fraction as well as in decimal form.

• Red color flowers are painted in the 5/12 or 0.4166 part of the cardboard.
• Green color flowers are painted in the 3/12 or 0.25 part of the cardboard.
• Orange color flowers are also painted in the 4/12 or 0.333 part of the cardboard.

Let us look at the fraction and decimal representation given in the chart below to have more clarity about the fraction to decimal conversion.

Let us now understand how to convert fraction to decimal using different methods.

There are two methods to convert fraction to decimal which are given below:

• Long division method
• By converting the denominator of the fraction into a power of 10

Convert Fraction to Decimal by Long Division Method

When a number is present in a fraction form i.e., p/q, we use the long division method to convert it into a decimal form. In such a case we divide the numerator by the denominator. Let us understand the steps involved in fraction to decimal conversion by the long division method with the help of an example.

Convert 4/19 to decimal.

• Step 1: In the given fraction 4/19, consider the numerator 4 as a dividend and the denominator 19 as the divisor. In this case, the denominator > numerator.
• Step 2: We have to make the dividend digit (4) greater than the numerator digit (19) by placing 0 next to 4 and to the quotient respectively. Now we have 40 as a new dividend. (40>19)
• Step 3: In the quotient part, it is important to insert decimal (.) after 0 and start the division.
• Step 4: Multiply 19 with a number so that the product is less than or equal to 40. We know that 19 times 2 is 38. The digit that appeared in the quotient is 2, and the remainder left is 2. After introducing decimal in the quotient we can introduce one 0 at each step of division.
• Step 5: Now the new dividend is 20. Multiply 19 with a number so that the product is less than or equal to 20. 19 times 1 is 19. Now the new digit in the quotient is 1 which makes it 0.21, and the remainder is 1.
• Step 6: Repeat the steps till we get 0 as the remainder or at least three decimal places in the quotient.

Try to read out the steps with the image given below for having a better understanding of converting fractions to decimals.

In the next section, let us discuss another method of the fraction to decimal conversion that is by converting the denominator into a power of 10.

Convert Fraction to Decimal by Changing the Denominator

Another method to convert the fraction to a decimal is by converting the denominator of the fraction to powers of 10 like 10, 100, 1000, etc. Following are the steps showing the procedure of the conversion of fractions to decimals by converting the denominator method.

Example: Convert 7/8 to decimals.

• Step 1: Firstly we have to think of a number by which we can multiply the denominator and numerator so that we can get a power of 10 in the denominator.
• Step 2: Here, the denominator is 8. (8 times 125 is 1000)
• Step 3: Now multiply the numerator and denominator with the same number, i.e., 125.
• Step 4: By multiplying the numerator of the fraction by 125, we get 7 × 125 = 875.
• Step 5: After completing the multiplication process we have a denominator in terms of the power of 10, i.e. 875/1000.
• Step 6: Insert a decimal point before the number of places equal to zeros in the denominator. Here, we have 3 zeros in the denominator, so we add the decimal point before three places counting from the right side. Thus, we get, 875/1000 = 0.875.

Note that this method is applicable only for the fractions whose denominator can be multiplied with a number to get a power of 10. For denominators that cannot be written as a power of 10, for example, 2/3, it is always better to use the long division method explained above.

Fraction to decimal chart is a direct approach to get the converted values easily. The chart gives us the values of some most commonly used fractions in terms of decimals and vice-versa. Fractions can be less than or greater than 1. Fractions that are less than 1 have a numerator < denominator. They are called proper fractions. The decimal values of proper fractions are always less than 1. Fractions that have a numerator ≥ denominator are called improper fractions. They have decimal values of 1 or more. Let us have more clarity about how the numbers will look like when we convert fractions to decimal form using the fraction to decimal chart given below:

Check out this article on Fraction to Decimal Chart for an in-depth understanding.

Check our fraction to decimal calculator and try a few conversions at your end. It is a free online tool that calculates the decimal form of a given fraction. This free online fraction to decimal calculator helps you to calculate the decimal value of fractions within a few seconds.

☛ Related Articles

Given below is the list of topics that are closely connected to fraction to decimal conversion.

• Relationship Between Fractions and Decimals
• Convert Decimal to Fraction
• Fraction to Percent
• Percent to Fraction

What is the Fraction to Decimal Conversion in Math?

Fraction to decimal in math is referred to as a procedure that we generally use to convert the fraction value to decimal value. While converting a fraction to a decimal, we divide the parts of fractions, i.e., the numerator is divided by the denominator. Decimal gives a more precise value as compared to fractions.

What is the Formula to Convert Fraction to Decimal?

The formula to convert a fraction to a decimal is given as "a ÷ b", where a is the numerator and b is the denominator of the fraction. In other words, the fraction to decimal formula states that we just need to divide the numerator by denominator to get the decimal equivalent of the fraction.

How to Convert a Fraction to a Decimal?

To convert a fraction to a decimal, we need to follow the steps given below.

• The numerator of the fraction will be treated as a dividend and the denominator as the divisor.
• If the numerator is less than the denominator add a decimal (point) along with 0 after the dividend.
• Perform the division.
• If the remainder keeps recurring, then the decimal can be stopped after a certain number of decimal places.
• For example, converting 4/5 to decimal gives 0.8.

What is the Result of Converting 22/7 Fraction to Decimal?

22/7 is an irrational number with 22 as the numerator and 7 as the denominator. On converting 22/7 into decimals, we get 3.14 up to two decimal places. It is a non-terminating non-repeating decimal number that extends up to infinity.

How to Convert 2/3 into Decimal Using the Fraction to Decimal Chart?

Using the fraction to decimal chart, the value of 2/3 is 0.666. To find the decimal value of 2/3 we perform the division operation until the remainder is 0 or up to 3-4 decimal places.

What Method is Used to Convert a Fraction to a Decimal?

There are two methods to convert a fraction to decimal form which are - division method and the method of changing the denominator to a power of 10.

How to Convert a Mixed Fraction to Decimal?

To convert a mixed fraction to a decimal, we first need to convert it into an improper fraction. Then divide the numerator by denominator to convert it into decimal form.

What is the Fraction to Decimal Conversion Chart?

A fraction to decimal conversion chart or table is a quick representation of decimal values of some commonly used fractions. For example, by using this chart, we can easily identify that 1/2 is the same as 0.5, 1/4 is the same as 0.25, and so on.

What is the Easiest Way to Convert a Fraction to a Decimal?

The easiest way to convert a fraction to a decimal is the division method. In this, we have to divide the numerator by the denominator of the fraction to get its decimal equivalent in the quotient.

What are the Steps to Convert a Fraction to a Decimal?

The steps to convert a fraction to decimal are given below:

• Step 1: Divide the numerator by the denominator.
• Step 2: Stop the division process when you get 0 in the remainder or three decimal places in the quotient.
• Step 3: The value obtained in the quotient will be our final answer in decimals.