Converting 0.12323 Repeating to a Fraction in Simplest Form
Introduction
Repeating decimals can be converted into fractions, and this process can be quite fascinating. In this article, we will explore how to convert the repeating decimal 0.12323 into a fraction in its simplest form.
The Process
To convert a repeating decimal into a fraction, we can use the following steps:
- Let the repeating decimal be represented by a variable, say x.
- Multiply both sides of the equation by 10^n, where n is the number of digits in the repeating part of the decimal.
- Subtract the original equation from the new equation.
- Simplify the resulting equation to get the fraction.
Applying the Process to 0.12323
Let's apply the process to our given decimal, 0.12323.
Step 1: Let x = 0.12323
x = 0.12323
Step 2: Multiply both sides by 100
100x = 12.32323
Step 3: Subtract the original equation from the new equation
100x = 12.32323 -x = -0.12323
99x = 12.2
Step 4: Simplify the equation
x = 12.2/99 x = 1220/990 x = 610/495
Simplifying Further
We can simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 5.
x = 122/99 x = 610/99
Result
Thus, the repeating decimal 0.12323 can be converted into a fraction in its simplest form, which is 610/99. This process demonstrates the fascinating connection between repeating decimals and fractions, and how we can use algebraic manipulations to convert between these two forms.
