0.135 Repeating Written as a Fraction
The decimal 0.135 repeating can be written as a fraction. But how do we do that?
Understanding Repeating Decimals
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In this case, the decimal 0.135 repeating means that the sequence "135" repeats indefinitely: 0.135135135...
Converting to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
- Let the repeating decimal be x.
- Multiply x by a power of 10 that is equal to the number of decimal places in the repeating sequence. In this case, we multiply x by 1000 (10^3) since the repeating sequence has 3 decimal places.
So, we get:
1000x = 135.135...
- Subtract x from both sides of the equation to get:
999x = 135
- Divide both sides of the equation by 999 to solve for x:
x = 135/999
Simplifying the Fraction
Now, we can simplify the fraction 135/999 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 135 and 999 is 27. So, we divide both numbers by 27:
x = (135 ÷ 27) / (999 ÷ 27) x = 5/37
Therefore, the decimal 0.135 repeating written as a fraction is 5/37.
I hope this helps! Let me know if you have any questions or need further clarification.
