Relationship Between Fractions and Decimals

The relationship between fractions and decimals is very important to understand to develop a strong base in arithmetic. When a number is represented in form of p/q, where p and q belong to whole numbers and q is not equal to 0, it is termed as a fraction and can be converted into a decimal form by either converting the denominator to a power of 10 or by long division method.

Both fractions and decimals are just two ways to represent numbers. Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part are connected through a decimal point, for example, 0.5. Fractions and decimals represent the relationship of part by whole. In both fractions and decimals, we represent the whole by 1. Let us look at some examples to understand the relationship between fractions and decimals. Consider a full-thin crust pizza with 6 slices. Your mother gave half of it, i.e., 3 slices then in fractional form, we write it as 1/2, and in the decimal form, we write it as 0.5.

Let us consider another example. Emma divides her garden into 12 equal parts. She grows flowers of different colors in each part of the garden. Amongst the 12 slots, she reserved 8 equal portions for red flowers, 2 portions for yellow color flowers, and 2 for blue color flowers. Let us write the portion given to flowers of each color in fraction and in decimal.

• Red flowers are grown in the 8/12 or 0.666 part of the garden.
• Yellow flowers are grown in the 2/12 or 0.1666 part of the garden.
• Blue flowers are also grown in the 2/12 or 0.1666 part of the garden.

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

We can convert a fraction to its decimal form by the following two methods.

• Long Division Method
• Convert the denominator of the fraction to multiples of 10 like 10, 100, 1000, etc.

Converting Fraction to Decimal by Long Division Method

When a number is present in a fraction form i.e., p/q, to convert it into the decimal form we use the long division method. The steps for converting fractions into decimals are given below. Let us understand these steps of the long division with the help of an example.

Convert 3/8 into decimals.

Step 1: Treat the numerator digit of the fraction as a dividend and the denominator as the divisor. In this case, the numerator is lesser than the denominator.
Step 2: Make the dividend greater than the numerator by placing 0 next to the digit and to the quotient. Now we have 30 as a new dividend. (30>8).
Step 3: In the quotient, place decimal after 0 and start the division.
Step 4: Multiply 8 with a number so that the product is less than equal to 30. 8 times 3 is 24. Here now the digit in the quotient is 3, the remainder is 6. After introducing decimal in the quotient we can attach one 0 at each step of division.
Step 5: Now the new dividend is 60. Multiply 8 with a number so that the product is less than equal to 60. 8 times 7 is 56. Here now quotient is 7, the remainder is 4.
Step 6: Now the new dividend is 40. Multiply 8 with a number so that the product is less than equal to 40. 8 times 5 is 40.
Step 7: The final remainder is 0 and the quotient is 0.375.
3/8 = 0.375.

Convert 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. Let us understand this with the steps given below. We will take an example to proceed with the given steps.

Convert 3/4 to decimals.

Step1: Think of a number by which we can easily multiply the denominator and numerator to get the power of 10.
Step2: Here denominator is 4. 4 times 25 is 100.
Step 3: Multiply the numerator also with the same number
Step 4: By multiplying the numerator of the fraction by 25 we get (3 × 25) = 75
Step 5: Now we have a denominator in terms of powers of 10.
Step 6: 75/100 = 0.75.
The decimal place of the final answer depends upon the number of trailing zeros present in the digit of the denominator.

Every decimal number can be expressed in the form of a fraction. Steps to convert a decimal number to the fractional form are stated below:

1. Rewrite the number by ignoring the decimal point.
2. 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.
3. Simplify the fraction.

Look at this example for a deeper understanding.

Decimal form = 6.5 = 65/10 = 13/2 (Fraction form of 6.5)

Important Notes:

1. Fractions represent a ratio between two numbers, so they show finite value. For example, 1/3, or we can say 1 out of 3 parts.
2. Decimals can also represent infinite values along with finite values. For example, if we convert the above fraction to decimal, we get 0.33333333 and it goes on up to infinity.

Related Articles

Check out the links of interesting articles related to the relationship between fractions and decimals.

• Fractions
• Decimals
• Long Division

What is the Importance of Fraction and Decimal?

Fractions and decimals are required when there is the precision required in the value because whole numbers can only be used for counting. For measuring, decimals and fractions are used. Decimal gives a more precise value as compared to fractions as we can even represent the infinite numbers using decimals, which is not possible with fractions.

What is the Difference Between the Fraction and Decimals?

The main difference between the fraction and decimals is that fraction represents a ratio between two, while decimals can also be used for writing infinite values and for more precision. Fractions are of the form p/q, where p and q are whole numbers and q is not equal to 0, while decimals are written with the help of a decimal point in between to separate the whole numbers part and the fractional part of a number, for example, 2.89 is a decimal number.

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.

How to Convert Decimals into Fractions?

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

What is 22/7 in Decimals?

22/7 is an irrational number, which is expressed as 3.14 in decimals up to two decimal places. It is a non-terminating and non-repeating decimal number that goes up to infinity.

What are the Ways to Convert Fraction to Decimal?

There are two ways to convert a fraction into a decimal, which are given below:

• Long division method
• Conversion of the denominator to powers of 10

How to Convert a Mixed Fraction to Decimal?

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