-as-a-fraction.jpeg "0.123 (13 Repeating) As A Fraction")
0.123 (13 Repeating) as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to convert 0.123 (13 repeating) into a fraction.
What is a Repeating Decimal?
A repeating decimal, also known as a recurring decimal, is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.123 (13 repeating), the sequence "13" repeats indefinitely.
Converting Repeating Decimals to Fractions
To convert a repeating decimal into a fraction, we can use the following steps:
- Let x be the repeating decimal: In this case, let x = 0.123 (13 repeating).
- Multiply both sides by 10^k: where k is the number of digits in the repeating sequence. In this case, k = 2, so we multiply both sides by 10^2 = 100.
This gives us:
100x = 12.313131...
- Subtract the original equation: Subtract x from both sides of the equation:
100x - x = 12.313131... - 0.123123...
This gives us:
99x = 12.19
- Divide both sides by the coefficient of x: In this case, the coefficient of x is 99, so we divide both sides by 99.
x = 12.19 / 99
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 12.19 and 99 is 1, so the fraction is already in its simplest form.
The Final Answer
Therefore, 0.123 (13 repeating) as a fraction is:
12.19 / 99
I hope this article has helped you learn how to convert a repeating decimal into a fraction!
