.083 3 Repeating as a Fraction
The decimal number .0833... is a repeating decimal, where the digits 3 repeat indefinitely. In this article, we will explore how to convert this repeating decimal to a fraction.
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use the following formula:
x = decimal number 10^n * x = decimal number with n decimal places
Where n is the number of decimal places that repeat.
Converting .0833... to a Fraction
Let's apply the formula to convert .0833... to a fraction.
Let x = .0833...
Since the digits 3 repeat every 3 decimal places, we can multiply both sides of the equation by 10^3:
10^3 * x = 10^3 * .0833... 1000x = 83.333...
Now, subtract x from both sides of the equation:
999x = 83.25 x = 83.25 / 999 x = 25/300 x = 1/12
So, .0833... as a fraction is 1/12.
Conclusion
In this article, we have learned how to convert a repeating decimal to a fraction using a simple formula. We applied this formula to convert .0833... to a fraction, which equals 1/12. This technique can be used to convert any repeating decimal to a fraction.
