Relationship Between Fractions and Decimals

Relationship Between Fractions and Decimals
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The relationship between fractions and decimals is very important to understand to develop a strong base in arithmetic.

In this mini-lesson, we will explore the relationship between fractions and decimals by learning how to convert fractions to decimals and decimals to fractions with the help of visualizations, interesting simulations, some solved examples, and a few interactive questions for you to test your understanding.

In the simulation given below, drag the points horizontally and vertically to shade a portion and observe its value in fraction and in decimal.

Lesson Plan

What Is the Relationship Between Fractions and Decimals?

Both fractions and decimals are just ways to represent numbers. Fractions are written in the form of \(\dfrac{p}{q}\), where \(q \neq 0\), while in decimals, the whole number part and fractional part is 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 whole by \(1\)

Let us look at some examples to understand the relationship between fraction and decimal.

Given below is an image of one half of a pizza. In fractional form, we write it as \(\dfrac{1}{2}\) and in decimal form we write it as \(0.5\) 

1/2 of a pizza

Emma divides her garden into 12 equal parts. She grows flowers of different colors in each part of the garden.

fraction and decimal of blue flowers in the garden

Let us write the portion given to flowers of each color in fraction and in decimal.

Red flowers are grown in \(\dfrac{8}{12}\) or \(0.666\) part of the garden.

Yellow flowers are grown in \(\dfrac{2}{12}\) or \(1.666\) part of the garden.

Blue flowers are also grown in \(\dfrac{2}{12}\) or \(1.666\) part of the garden.

Let us look at the fraction and decimal chart to have more clarity about the relationship between fractions and decimals.

fraction and decimal chart

Now, let us look at the fractional and decimal equivalents of some commonly used values.

Fractional Value Decimal Value
\(\dfrac{1}{2}\) \(0.5\)
\(\dfrac{1}{3}\) \(0.33\)
\(\dfrac{1}{4}\) \(0.25\)
\(\dfrac{1}{6}\) \(0.166\)
\(\dfrac{1}{7}\) \(0.14\)
\(\dfrac{1}{8}\) \(0.125\)
\(\dfrac{1}{9}\) \(0.11\)
\(\dfrac{1}{10}\) \(0.1\)
\(\dfrac{1}{20}\) \(0.05\)
\(\dfrac{1}{25}\) \(0.04\)
\(\dfrac{1}{50}\) \(0.02\)

How to Convert Fraction into Decimal?

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

  • Long Division Method

Conversion of decimal numbers

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

convert fraction to decimal

Answer

Fraction to Decimal Calculator

In the simulation given below, write any fraction and click on "Convert" to find its decimal equivalent.


How to Convert Decimal into Fraction?

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 place value of the last digit in the fractional part of the number.
  3. Simplify the fraction.

Look at this example for a deeper understanding.

convert decimal to fraction

Decimal to Fraction Calculator

Decimal to fraction conversion calculator makes calculations easy. 

In the simulation given below, write any decimal number and click on "Convert" to find the fraction equivalent to it.

 
important notes to remember
Important Notes
  1. Fractions represent a ratio between two numbers, so they show finite value. For example, \(\dfrac{1}{3}\) 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.

Solved Examples

Example 1

 

 

For the following figure, what is the decimal representation of the yellow shaded portion of the red square?

Find fractional and decimal value

Solution

In the given figure, 1 out of 4 red-colored squares is shaded yellow.

So, the fraction of the yellow shaded portion of the red square is \(\dfrac{1}{4}\).

To convert it into a decimal, we need to multiply both numerator and denominator by \(25\), so that we will have a power of 10 in the denominator.

\(\dfrac{1}{4}\times \dfrac{25}{25}=\dfrac{25}{100}=0.25\)

\(\therefore 0.25\) or \(\dfrac{1}{4}\)portion of the red square is shaded yellow.
Example 2

 

 

Jim bought \(100\) apples from a nearby fruit vendor but later found out that \(5\) of them were rotten. Can you tell the fraction and the decimal value of the rotten apples to the total apples bought by Jim?

Solution

Here, we have \(5\) rotten apples out of \(100\).

So our fraction becomes

\(\dfrac{5}{100}\)

How do we write it as decimal?

Such problems are solved by dividing the numerator by the denominator.

Here, we need to divide 5 by 100

To divide 5 by 100, we will simply shift it by 2 decimal places on the right.

The number of decimal places we can shift in the numerator depends upon the trailing zeroes the whole number in the denominator has.
Thus, after division, we get:

\(\dfrac{5}{100}=0.05\)

\(\therefore\) Ratio of rotten apples to the fresh apples in decimal form is \(0.05\)
Example 3

 

 

What part of the strip is shaded? Write your answer in decimal form. 

Visualizing fractions and decimals using a strip

Solution

As we can see that in fraction, \(\dfrac{1}{3}\) part of the strip is shaded.

Now, we divide the numerator by denominator to convert it into decimal.

converting fraction to decimal

 We will round decimal up to 3 places to write an approximate answer.

\(\therefore 0.333\) part of the strip is shaded.
Example 4

 

 

There are \(36\) fruits in a basket. \(9\) are mangoes and the remaining are apples. What fraction of the fruits are apples? Write your answer in decimal too.

fraction of apples in basket

Solution

Total number of fruits in the basket = \(36\)

Number of mangoes = \(9\)

Number of apples = \(36-9=27\) apples

\(\therefore\) Fraction of apples in the basket is \(\dfrac{27}{36}\) and in simplest form, \(\dfrac{3}{4}\)

Now, we have to convert \(\dfrac{3}{4}\) into decimal.

To convert \(\dfrac{3}{4}\) into decimal, we multiply both numerator and denominator by \(25\) to get a power of 10 in the denominator. 

\(\dfrac{3}{4} \times \dfrac{25}{25}=\dfrac{75}{100}\)

\(\dfrac{75}{100}=0.75\)

\(\therefore\ 0.75\) or \(\dfrac{3}{4}\) fruits in the basket are apples.
 
Challenge your math skills
Challenging Questions
  1. Can you find out what decimal is a second to an hour?
  2. How many tenths make one complete unit?
  3. Can we express irrational numbers in decimal form? If yes, write \(\dfrac{22}{7}\) in decimals.

Now, try to solve interactive questions given below taken from the relationship between fractions and decimals worksheets designed by our experts for you to practice.

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 

Let's Summarize

The mini-lesson targeted the fascinating concept of the relationship between fractions and decimals. The math journey around the relationship between fractions and decimals starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that is not only irrelatable and easy to grasp but will also stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions (FAQs)

1. What is the importance of fraction and decimal?

Fractions and decimals are required when there is a precision required in the value because whole numbers can only be used for counting. For measuring, decimals and fractions are used.

2. 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 be used for writing infinite values and for more precision.

3. How are decimal and fractions represented?

Fractions are written in the form of \(\dfrac{p}{q}\), where \(q \neq 0\), while in decimals, whole number part and fractional part is connected through a decimal point, for example, \(0.5\).

4. How to convert decimals into fractions?

To convert a decimal to 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

5. What is 22/7 in decimals?

\(\dfrac{22}{7}\) is an irrational number, which is expressed as \(3.14\) in decimals up to two decimal places.

6. 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 denominator to powers of 10

7. 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.

  
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