0.13 Repeating Decimal as a Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.13, where the digits 13 repeat indefinitely. But, have you ever wondered how to convert this repeating decimal into a fraction?
The Problem
Converting a repeating decimal into a fraction can be a bit tricky. However, with a simple trick, we can convert 0.13 into a fraction.
The Solution
Let's say we have the equation:
x = 0.131313...
We can multiply both sides of the equation by 100 to get:
100x = 13.131313...
Now, subtract the original equation from the new equation:
100x - x = 13.131313... - 0.131313...
This simplifies to:
99x = 13
Now, divide both sides by 99:
x = 13/99
So, the fraction equivalent of the repeating decimal 0.13 is 13/99.
Checking the Answer
To check our answer, we can convert the fraction back into a decimal:
13/99 = 0.131313...
Voila! Our answer is correct.
Conclusion
In conclusion, converting a repeating decimal into a fraction can be a simple process. By multiplying the equation by a power of 10, subtracting the original equation, and then dividing by the difference, we can convert any repeating decimal into a fraction. In this case, we converted 0.13 into 13/99.
