0.083 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is the decimal 0.083, which is a repeating decimal. But have you ever wondered what 0.083 repeating as a fraction looks like?
Converting 0.083 to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
- Let the repeating decimal be x.
- Multiply both sides of the equation by 10 raised to the power of the number of digits in the repeating part.
- Subtract the original equation from the new equation.
- Simplify the resulting equation to get the fraction.
Let's apply these steps to 0.083:
Step 1: Let x = 0.083 x = 0.083
Step 2: Multiply by 10^3 (since the repeating part has 3 digits) 1000x = 83.083
Step 3: Subtract the original equation 1000x - x = 83.083 - 0.083 999x = 83
Step 4: Simplify x = 83/999
Therefore, 0.083 repeating as a fraction is equal to 83/999.
Simplifying the Fraction
We can further simplify the fraction 83/999 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 83 and 999 is 1, so the fraction is already in its simplest form.
Conclusion
In conclusion, 0.083 repeating as a fraction is equal to 83/999. By using the steps outlined above, we can convert any repeating decimal to a fraction, which can be useful in various mathematical applications.
