0.083 3 Repeating as a Fraction
In this article, we will discuss how to convert the repeating decimal 0.083 3 to a fraction.
Repeating Decimal
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In this case, the repeating decimal is 0.083 3, where the sequence "3" repeats indefinitely.
Conversion to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
Step 1: Let x = 0.083 3
Let's assume that x = 0.083 3.
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal points.
100x = 8.33 3
Step 3: Subtract the original equation from the new equation
Subtract the original equation from the new equation to eliminate the repeating decimal part.
100x - x = 8.33 3 - 0.083 3
This simplifies to:
99x = 8.25
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to solve for x.
x = 8.25 / 99
x = 25 / 300
x = 1 / 12
Therefore, the repeating decimal 0.083 3 is equal to the fraction 1 / 12.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.083 3 to a fraction, which is 1 / 12. This method can be applied to any repeating decimal to convert it to a fraction.
