Converting 0.123 23 Repeating to a Fraction
Have you ever wondered how to convert a repeating decimal like 0.123 23 to a fraction? It's actually quite simple, and in this article, we'll show you how to do it.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.123 23, the sequence "23" repeats indefinitely. This type of decimal is also known as a recurring decimal.
Converting 0.123 23 to a Fraction
To convert 0.123 23 to a fraction, we can use the following steps:
Step 1: Identify the Repeating Sequence
The first step is to identify the repeating sequence in the decimal. In this case, the repeating sequence is "23".
Step 2: Create an Equation
Let's say the repeating decimal is equal to x. We can set up an equation as follows:
x = 0.123 23
Step 3: Multiply by 100
Multiply both sides of the equation by 100 to get:
100x = 12.323 23
Step 4: Subtract the Original Equation
Subtract the original equation from the new equation:
100x - x = 12.323 23 - 0.123 23
This simplifies to:
99x = 12.2
Step 5: Solve for x
Divide both sides of the equation by 99 to solve for x:
x = 12.2/99
x = 122/990
x = 61/495
The Final Answer
Therefore, the fraction equivalent to 0.123 23 is:
61/495
And that's it! We've successfully converted the repeating decimal 0.123 23 to a fraction.
I hope this article has helped you understand how to convert a repeating decimal to a fraction. If you have any more questions or need further clarification, feel free to ask!
