The first part of converting to a fraction involves writing the given decimal, which is normally represented in the form of a fraction, with denominator 1. Then we multiply both the numerator and denominator with the multiples of 10, to remove decimal point (.) A decimal number such as 1.7 would be equivalent to a fraction of 17/10. We cannot merely divide 17/10 further. Decimal numbers in the context of computers are those with base 10, but decimal numbers in mathematics are those with a dot (.) between their digits. A decimal is nothing more than a fraction with a denominator of 10 or a multiple of 10. Examples include 5.6, 12.6, 60.7, 1.28, 8.432, etc.
The process of converting decimal to fraction is very easy. As fractions and decimal equivalence, both are useful for expressing partial numbers. In the same way, you can express a fraction as a decimal, and vice-versa. By dividing the numerator with the denominator, a fraction can be converted into a decimal. Also, it is possible to express a fraction as a decimal by performing the division of the ratio. Fractions are parts of whole numbers. They are expressed as a ratio of two numbers, a/b, where a and b are both integers and a is not equal to b.
Steps to convert decimal into a fraction:
- To begin writing the given decimal as a ratio, first write p/q, where q is equal to 1.
- The numerator and denominator are to be multiplied by multiples of 10, for every decimal, so that each decimal in the numerator becomes a whole number. (If there are two decimal places, add 100/100)
- Simply the resulting fraction
Conversion of recurring decimal into a fraction:
In many cases, changing a decimal number to a fraction is an easy task. However, converting repeating and recurring numbers to fractions can be cumbersome. For instance, 0.555…, 8.12222…, and 0.43777… are repeating numbers.
For example: Convert 0.5555… Into fraction
Ans: Let x = 0.5555
Now multiply x by 10 on both sides.
10 x = 5.555…
Subtracting x from 10x, we get;
10x-x = 5.555…- 0.5555
9x = 5.000
X = 5/9
Hence, 0.5555 = 5/9
Practical problems on the conversion of a decimal to a fraction:
1. Find the fraction form of the decimal 0.9
Ans: Given, decimal number 0.8, we need to find the fraction for 0.9
We can also find several equivalent fractions by finding their multiples.
0.9 = 9/10
Now multiply, 9/10 by 2, both in numerator and denominator, then we get;
(9×2)/(10×2) = 18/20
To find more equivalent fractions, let us multiply 9/10 by 5 and 10 both in numerator and denominator.
9×5/10×5 = 45/50
9×10/10×10 = 90/100
Therefore, the fractions of 0.9 decimal are 9/10, 45/50, 90/100
2. Convert 3.15 into a fraction
Ans: Given, 3.15 is a decimal number.
Multiply and divide 3.15 by 100.
3.15 × 100/100 = 315/100
If we simplify it more, we get;
We can also find the equivalent fractions by multiplying the numerator and the denominator by 2. Such as;
63×2/20×2 = 126/40
So, 3.15 equivalent fractions are 315/100, 63/20, and 126/40.
3. Convert 1.625 into a mixed fraction.
Ans: We can write 1.625 as 1.625/1
Multiply by 1000 to remove decimal up to three places
1.625/1 x (1000/1000) = 1625/1000
Simplifying 1625/1000 we get;
Now converting into a mixed fraction.
13/8 = 1 5/8
Hence, 1 5/8 is the mixed fraction equivalent to 1.625
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