# Convert decimal into fraction

In this post we learn how to convert decimal number into fraction.
After studying the concept we will move on to solve problems related to the concept

## Decimal To Fraction

Suppose a decimal number is given to you

In order to convert it into fraction, follow the below step

Step 01
Insert 1 as denominator

Step 02
Count number of digits after decimal
In the below number, there are two digits after decimal

Step 03
Remove the decimal and insert two zeros in the denominator

Step 04
If possible, simplify (or reduce) the fraction

This is not possible in this case.

Hence we have converted decimal into fraction
1.53 ⟹ \frac{153}{100} \\\ \\

You can see that method is very simple and straight forward.
Let us see some other examples for conceptual clarity

Example 02
Convert 0.652 into fraction

Step 01
Insert 1 in denominator

Step 02
Count number of digits after decimal
You can see there are three numbers after decimal

Step 03
Remove the decimal and insert three zeros in denominator

Step 04
Further Simplify the fraction (if possible)

Hence the decimal 0.652 is converted into \frac{163}{25} \\\ \\

Example 03
Convert 0.000255 into fraction

Step 01
Insert 1 as denominator

Step 02
Count the number of digits after decimal
There are 6 digits after decimal

Step 03
Remove the decimal and insert six zeros in denominator

Step 04
Simplify the fraction as much as possible

Hence the decimal 0.000255 is converted into \frac{51}{200000} \\\ \\

Example 04
101.007 intro fraction

Step 01
Insert 1 as denominator

Step 02
Count number of digits after decimal
You can see there are three digits after decimal

Step 03
Remove the decimal and insert three zeros in denominator

Step 4
Further simplify the fraction (if possible)

Further simplification is not possible

Hence the decimal 101.007 is converted into \frac{101007}{1000} \\\ \\

### Special Case of Recurring Number

Example 05
Find the fraction of recurring decimal
x = 0.3333 . . . . . . .

Step 01
Insert 1 in the denominator

Step 02
Multiply numerator and denominator by 3

As 0. 9999…. is very close to 1.
It can be assumed that 0.999.. = 1

Hence the fraction will be

## Decimal into Fraction Worksheet

Below is the collection of question related to topic Decimal into Fraction

All the questions are to the standard of Grade 5

Each questions are provided with solution

(01) Convert 0.5 to Fraction

\Longrightarrow \ \frac{0.5}{1}\\\ \\ \Longrightarrow \ \frac{5}{10}\\\ \\ \Longrightarrow \ \frac{5\div 5}{10\div 5}\\\ \\ \Longrightarrow \frac{1}{2}

(02) Convert 0.625 to fraction

\Longrightarrow \ \frac{0.625}{1}\\\ \\ \Longrightarrow \ \frac{625}{1000}\\\ \\

Hence 5/8 is the required fraction

(03) Convert 23.909 to fraction

\Longrightarrow \ \frac{23.909}{1}\\\ \\ \Longrightarrow \ \frac{23909}{1000}\\\ \\

(04) Convert 80.05 into fraction form

\Longrightarrow \ \frac{80.05}{1}\\\ \\ \Longrightarrow \ \frac{8005}{100} \\\ \\

Hence 1601/20 is the solution

(05) Convert the decimal 31.2 into fraction

\Longrightarrow \ \frac{31.2}{1}\\\ \\ \Longrightarrow \ \frac{312}{10}\\\ \\

Simplifying the fraction

Hence 156/5 is the solution

(06) Convert the decimal 100.25 into fraction

\Longrightarrow \ \frac{100.25}{1}\\\ \\ \Longrightarrow \ \frac{10025}{100}

Simplifying the fraction

401/4 is the required fraction

(07) Convert 0.53 into fraction

\Longrightarrow \ \frac{0.53}{1}\\\ \\ \Longrightarrow \ \frac{53}{100}\

53/100 is the required fraction

(08) Convert 1.512 into fraction

\Longrightarrow \ \frac{1.512}{1}\\\ \\ \Longrightarrow \ \frac{1512}{1000}\

188/125 is the required fraction

(09) Convert 0.00013 into fraction

\Longrightarrow \ \frac{0.00013}{1}\\\ \\ \Longrightarrow \ \frac{13}{100000}\\\ \\

Hence 13/100000 is the solution

(10) Convert 99.504 into fraction

\Longrightarrow \ \frac{99.504}{1}\\\ \\ \Longrightarrow \ \frac{99504}{1000}\\\ \\

12438/125 is the required fraction

(01) What is the fraction for 0.72

(a) 17/25
(b) 18/25
(c) 19/25
(d) 21/25

\Longrightarrow \ \frac{0.72}{1}\\\ \\ \Longrightarrow \ \frac{72}{100}\

Option (b) is the right answer

(02) Select the fraction for 1.65

(a) 9/25
(b) 7/25
(c) 17/25
(d) 33/25

\Longrightarrow \ \frac{1.65}{1}\\\ \\ \Longrightarrow \ \frac{165}{100}\

option (d) is the right answer

(03) Select the right fraction for 0.06

(a) 3/50
(b) 7/50
(c) 11/50
(d) 1/50

\Longrightarrow \ \frac{0.06}{1}\\\ \\ \Longrightarrow \ \frac{6}{100}\

Option (a) is the right answer

(04) Find the fraction of 5.055

(a) 1011/100
(b) 1011/200
(c) 1013/300
(d) 1017/200

\Longrightarrow \ \frac{5.055}{1}\\\ \\ \Longrightarrow \ \frac{5055}{1000}\

Option (b) is the right answer

(05) What is the right fraction of 0.7

(a) 1/10
(b) 7/100
(c) 7/10
(d) 7/1000

\Longrightarrow \ \frac{0.7}{1}\\\ \\ \Longrightarrow \ \frac{7}{10}\

Option (c) is the right answer

(06) Find the fraction of number 0.48

(a) 48/25
(b) 12/35
(c) 10/13
(d) 12/25

\Longrightarrow \ \frac{0.48}{1}\\\ \\ \Longrightarrow \ \frac{48}{100}\

Option (d) is the right answer

(07) Find the fraction for decimal 0.091

(a) 91/100
(b) 91/1000
(c) 91/10
(d) 91/10000

\Longrightarrow \ \frac{0.091}{1}\\\ \\ \Longrightarrow \ \frac{91}{1000}\

Option (b) is the right answer

(08) Find the fraction for 0.5

(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/10

\Longrightarrow \ \frac{0.5}{1}\\\ \\ \Longrightarrow \ \frac{5}{10}\

Option (b) is the right answer

(09) Find the fraction for decimal 10.03

(a) 1003/10
(b) 1003/1000
(c) 1003/10000
(d) 1003/100

\Longrightarrow \ \frac{10.03}{1}\\\ \\ \Longrightarrow \ \frac{1003}{100}\

Option (d) is the solution

(10) Find the fraction for decimal 1.3

(a) 13/10
(b) 13/100
(c) 13/1000
(d) 13/10000