How to Convert a Decimal to a Fraction :
In this section, you will learn, how to convert a decimal to a fraction.
Usually we have two kind of decimals.
Terminating decimal |
Non terminating and recurring decimal | |
A decimal which ends with countable number of digits is known as terminating decimal. For example, 0.25, 0.5, ............... etc |
Non terminating decimal means, it will not end up with any number. For example, 0.525252.............. 0.125125.............. |
To convert a terminating decimal to fraction, we have to follow the steps given below.
Step 1 :
First count the number of digits after the decimal point.
Step 2 :
By multiplying by 10, 100, 1000, ......... etc, we may get rid of the decimal point.
Fro example, if we have only two digits after the decimal point, we have to multiply both numerator and denominator by 100.
Step 3 :
If it is possible, we may simplify the numerator and denominator separately.
To know, how to convert a non-terminating recurring decimal to fraction,
Example 1 :
Convert the following decimal number in the form p/q, where p and q are and q ≠ 0.
0.35
Solution :
Number of digits after the decimal point is 2.
So, we have to multiply both numerator and denominator by 100.
0.35 x (100/100) = 35/100
We may simplify both numerator and denominator by 5 times table.
= 7/20
Hence the fraction form of the decimal 0.35 is 7/20.
Example 2 :
Convert the following decimal number in the form p/q, where p and q are and q ≠ 0.
2.176
Solution :
Number of digits after the decimal point is 3.
So, we have to multiply both numerator and denominator by 1000.
2.176 x (1000/1000) = 2176/1000
We may simplify both numerator and denominator
= 1088/500
= 544/250
= 272/125
Hence the fraction form of the decimal 2.176 is 272/125.
Example 3 :
Covert the given repeating decimal into fraction
0.33333.............
Solution :
Let x = 0.3333........... (1)
Number of digits in the repeating pattern is 1. That is 3.
Because there is only one digit in the repeating pattern, multiply both sides of (1) by 10.
10x = 3.333......... (2)
(2) - (1) ==>
10x - x = 3.333.........00
9x = 3
Divide each side by 9.
x = 3/9
x = 1/3
Hence the fraction form of the decimal 0.333..... is 1/3.
Example 4 :
Covert the given repeating decimal into fraction
0.6868.........
Solution :
Let x = 0.6868........... (1)
Number of digits in the repeating pattern is 2. That is 68.
Because there are two digits in the repeating pattern, multiply both sides of (1) by 100.
100x = 68.6868............... (2)
(2) - (1)==>
100x - x = 68.6868.........0
99x = 68
Divide each side by 99.
x = 68/99
Hence the fraction form of the decimal 0.6868...is 68/99.
Example 5 :
Covert the given repeating decimal into fraction
32.03256256256..........
Solution :
Let x = 32.03256256256.............
Here, the repeated pattern is 256
No. of digits between the 1st repeated pattern and decimal is 2.
So, multiply the given decimal by 100. Then, we have
100x = 3203.256256256...............(1)
No. of digits between the 2nd repeated pattern and decimal = 5
So, multiply the given decimal by 100000. Then, we have
100000x = 3203256.256256256...............(2)
Subtracting (1) from (2), we get
(2) - (1) ===>
99900x = 3200053
x = 3200053/99900
Hence the fraction form of the decimal 32.03256256256. .......is 3200053/99900.
After having gone through the stuff given above, we hope that the students would have understood, how to convert a decimal to a fraction.
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