How to convert a decimal to a fraction :
Here we are going to see 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 convert a non terminating recurring decimal to fraction, we have to follow the steps given below.
Step 1 :
Assume the given question as "x"
Step 2 :
Count the repeating number of digits, based on this number we have to multiply both sides by 10, 100, ...... etc.
For example, if the repeating number of digits is 3, we have multiply both sides by 1000.
Step 3 :
By subtracting the first equation from the second equation, we get the answer.
Let us look into some examples to understand how to convert the decimal into 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)
Repeating number of digits = 1
Multiply both sides by 10,
10x = 3.333......... (2)
(2) - (1) ==> 10x - x = 3.333.........000000000000000000
0000000000000000= 0.333..........000000000000000000
0000000000________________000000000000000000
0000000000000009x = 3.00000000000000000000000
Divide by 9 on both sides
x = 3/9
x = 1/3
Example 4 :
Covert the given repeating decimal into fraction
0.56868.........
Solution :
Let x = 0.56868........... (1)
Repeating number of digits = 2
Multiply both sides by 100,
100x = 56.868............... (2)
(2) - (1)==> 100x - x = 56.868.........00000000000000000
00000000000000000= 0.568..........0000000000000000
0000000000________________000000000000000000
00000000000099x = 56.300000000000000000000000
99x = 56.3
Divide by 99 on both sides
x = 56.3/99
Multiply both numerator and denominator by 10
x = (56.3/99) x (10/10)
x = 563/990
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