0.138 Recurring as a Fraction
Have you ever wondered how to convert a recurring decimal into a fraction? In this article, we'll explore how to convert 0.138 recurring into a fraction.
What is a Recurring Decimal?
A recurring decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.138 recurring is a recurring decimal because the sequence "138" repeats indefinitely: 0.138138138...
Converting 0.138 Recurring into a Fraction
To convert 0.138 recurring into a fraction, we can use the following method:
Let x = 0.138138...
Multiply both sides by 1000 (because the recurring sequence has 3 digits):
1000x = 138.138138...
Subtract the original equation from the new equation:
1000x - x = 138.138138... - 0.138138...
This simplifies to:
999x = 138
Now, divide both sides by 999:
x = 138/999
Simplifying the Fraction
We can simplify the fraction 138/999 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 138 and 999 is 3, so we can divide both numbers by 3:
x = (138 ÷ 3) / (999 ÷ 3) x = 46/333
The Final Answer
So, 0.138 recurring as a fraction is equal to 46/333.
I hope this helps! Let me know if you have any questions.
