0.083 Repeating as a Fraction Simplified
When we encounter a repeating decimal, it can be challenging to simplify it as a fraction. However, there are steps we can follow to convert a repeating decimal to a simplified fraction. In this article, we will explore how to convert 0.083 repeating as a fraction simplified.
Step 1: Write the Repeating Decimal
Let's start by writing the repeating decimal: 0.083 repeating.
Step 2: Identify the Pattern
The pattern in this repeating decimal is "083" repeating every three digits.
Step 3: Convert to a Fraction
To convert the repeating decimal to a fraction, we can set up an equation using the pattern:
Let x = 0.083 repeating
Since the pattern repeats every three digits, we can multiply both sides of the equation by 1000 to shift the decimal point:
1000x = 83.083 repeating
Now, subtract the original equation from the new equation:
1000x - x = 83.083 - 0.083 999x = 83
Step 4: Simplify the Fraction
Now, divide both sides of the equation by 999 to simplify the fraction:
x = 83/999
So, 0.083 repeating as a fraction simplified is 83/999.
Conclusion
In conclusion, we have successfully converted 0.083 repeating as a fraction simplified to 83/999. By following these steps, you can convert any repeating decimal to a simplified fraction.
