.008 Repeating as a Fraction
In this article, we will explore how to convert the repeating decimal .008 into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of .008, the sequence "008" repeats indefinitely, making it a repeating decimal.
Converting .008 Repeating to a Fraction
To convert .008 repeating to a fraction, we can use the following steps:
- Let x = .008 (assign the repeating decimal to a variable x)
- Multiply both sides by 1000 (this will eliminate the decimal point and make it easier to work with)
1000x = 8.008
- subtract x from both sides (this will eliminate the repeating decimal on the right side of the equation)
999x = 8
- Divide both sides by 999 (this will give us the fraction)
x = 8/999
Therefore, .008 repeating as a fraction is equal to 8/999.
Simplifying the Fraction
The fraction 8/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 8 and 999 is 1, so the simplified fraction is still 8/999.
Conclusion
In conclusion, .008 repeating as a fraction is equal to 8/999. This fraction can be useful in various mathematical applications, such as converting between decimal and fractional representations of numbers.
