Convert Decimal to Fraction

Converting decimals to fractions is one of the most frequently carried out steps in arithmetic. However, in order to do so, you need to have your division basics in place. Once you grasp this, you will be able to convert decimals to fractions, as well as fractions to decimals.

Check out the decimal to fraction table in this lesson to get a better idea of how you can convert decimals into fractions.

Here is a simple 4-step process to convert any decimal into a fraction.

Steps for Conversion:

• Step 1- Identify the place value of the digits after the decimal, in the number.
• Step 2- Use that to determine what the denominator of the fraction would be.
• Step 3- Remove the decimal point. Re-write in the fraction form and simplify it.
• Step 4- Express in terms of the lowest Equivalent fraction.

Let us look at an example to understand these steps.

Example: Convert 0.5 into a fraction.

Solution: Let's apply the steps that we learned.

Step 1: Identify the place value of the last digit.

0.5 <------------ 5 is in the tenths place. (0.5 indicates 0.50)

Step 2: The denominator would be 10

Step 3: Fraction format: Numerator/Denominator = 5/10

Step 4: Simplest Form: 1/2

Thus, 0.5=5/10=1/2.

Go through the sections below to find more examples on how to convert fractions to decimals. There are three individual cases that you might come across while converting decimal to fraction, and those are listed below:

• Converting Repeating Decimal to Fraction
• Converting Decimals to Mixed Number Fractions
• Convert Negative Decimal to a Fraction

Let's learn about each case in detail.

Converting Repeating Decimal to Fraction

Repeating decimals are those that do not end after a finite number of decimal places and some particular digits or a single digit after the decimal point keep on repeating in the number. To convert any repeating decimal to a fraction, there is a particular method that needs to be applied. Let's consider an example to understand that.

Convert 0.77777... to a fraction.

Let x = recurring number, i.e.

0.77777....

n= the number of recurring digits, i.e. 7

Multiply the recurring decimal by 10, i.e.,

10x=7.77777...

This implies,

10x - x=7
9x=7
∴ x= 7/9

Converting Decimals to Mixed Number Fractions

Decimals with values greater than 1 can be written as mixed fractions. Look at the steps to convert such decimal numbers into mixed fraction form:

• Step 1- Consider the whole number part and decimal part in the given decimal number separately.
• Step 2- Write the decimal part in the fractional form by ignoring the decimal point and dividing it by a power of 10 in which there is the same number of zeros as the decimal places.
• Step 3- Simplify the fraction obtained.
• Step 4- Attach the whole number part of the original number with the fraction obtained in step 3. That would be your answer.

Let's consider an example.

Convert 2.5 into a mixed fraction.

• Step 1: Consider 2 and 0.5 as separate entities.
• Step 2: 0.5 can be written as 5/10 (as a fraction).
• Step 3: 5/10 = 1/2 (in the simplified form).
• Step 4: 2+1/2= \(2\dfrac{1}{2}\)

∴ 2.5 can be wriiten as \(2\dfrac{1}{2}\) as fraction.

Convert Negative Decimal to a Fraction

To convert any negative decimal number to a fraction, we follow the steps given below:

• Step 1: Remove the negative sign from the decimal number.
• Step 2: Perform the conversion on the positive value.
• Step 3: Apply the negative sign to the fraction answer.

For example, convert -3.2 into a fraction.

• Step 1: Remove the negative sign. Consider it as 3.2
• Step 2: There is one digit after the fraction, so multiply and divide 3.2 by 10.
• Step 3: Convert 32/10 to its lowest form and apply a negative sign to the fraction answer.

Thus, the answer is -16/5.

The decimal to fraction conversion table below shows some commonly-used fractions and their decimal equivalents.

This is the tabular way of showing the conversion of decimal to its equivalent fraction. Now, look at the chart given below and understand it visually.

Decimal and Fractions are used to represent inches values. To convert a given inch measurement from decimals to fractions, we have to focus on the fractional part of the decimal number. For example, if we have to convert 6.25 inches to its fractional equivalent, it has 6 in the whole number part and 0.25 in the fractional part. 0.25 has two digits after the decimal point, so it can be written as 25/100 as a fraction, which can be reduced to 1/4. Therefore, we get 6.25= 6 1/4 inches. This is how we convert inches from decimal to fraction.

Process to Convert Decimal to Fraction Inches

A fractional inch value like 36.125 inches includes 3 feet and an additional 0.125 inches. There are three digits after the decimal. Hence, multiply and divide 0.125 by 1000. For 0.125, the best option is 1/8 of an inch. Therefore, the height will be \( 3\dfrac{1}{8} \)" in.

Points to Remember:

Procedure to convert decimal to fraction:

1. Identify the place value of the last digit in the number.
2. Use that to determine what the denominator of the fraction would be.
3. Remove the decimal point. Re-write in the fraction form and simplify it.
4. Express in terms of the lowest Equivalent fraction.

☛Related Articles

Check out few more interesting articles related to decimal to fraction conversion.

• Fraction to Decimal
• Fraction to Decimal Chart
• Decimal to Fraction Calculator

What is Decimal to Fraction Conversion?

Decimal to fraction conversion is a procedure of writing decimal values in the form of fraction value and vice-versa. To convert the number from decimal to fraction form we divide the number by the power of 10 such that the number of zeros in that should be equal to the number of decimal places in the given number and simplify the fraction. For example, decimal form = 7.5 = 75/10 = 15/2 (fraction form of 7.5).

How to Convert Decimal to Fraction?

To convert a decimal to a fraction, we follow three basic steps mentioned below:

• Rewrite the number by ignoring the decimal point.
• Divide the number by the place value of the last digit in the fractional part of the number.
• Simplify the fraction.

How to Convert Fractions to Decimal?

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

What is the Difference Between the Fraction and the Decimal?

The main difference between the fraction and decimals is that fraction represents a ratio between two, while decimals can be used for writing infinite values and for more precision.

How to Convert Mixed Fraction to Decimals?

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

What is the Use of Decimal to Fraction Chart?

When we represent decimal value into a fraction (p/q) form we use decimal to fraction chart for easy and fast calculations. It also helps in the opposite conversion that is converting fraction to decimal as well.

☛ Check now for more practice:

• Decimal to Fraction Calculator
• Fraction to Decimal Calculator
• Converting Decimal to Fraction Worksheets

How Do you Write 0.25 Decimal Value as a Fraction?

Let's see how to convert 0.25 into fraction step-wise:

• Step 1: Count the numbers after the decimal point.
• Step 2: There are two digits after the decimal point. Hence, multiply and divide 0.25 by 100.
• Step 3: Simplify 25/100 to its lowest form, that is 1/4.

Thus, 1/4 is the fraction form of 0.25.

What are Repeating and Non-Repeating Decimals?

Repeating Decimals are those in which one or more digits repeat again and again, for example, 1/3=0.333333....., while non-repeating decimals are those that end after a specific number of digits, for example, 1/2=0.5.

How are Decimal and Fractions Represented?

Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part is connected through a decimal point, for example, 0.5.