0.05 Repeating as a Fraction
What is 0.05 Repeating?
The decimal number 0.05 repeating, also written as 0.050505..., is a non-terminating and recurring decimal. This means that the decimal expansion goes on indefinitely in a repetitive pattern.
Converting 0.05 Repeating to a Fraction
To convert 0.05 repeating to a fraction, we can use a simple trick. Let's multiply the number by 100 to get:
100x = 5.050505...
Now, subtract the original number from the new number:
100x - x = 5.050505... - 0.050505... 99x = 5
Divide both sides by 99:
x = 5/99
So, the fraction equivalent of 0.05 repeating is 5/99.
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 5 and 99 is 1.
Therefore, the simplified fraction is still 5/99.
Conclusion
In this article, we have successfully converted the repeating decimal 0.05 to a fraction, which is 5/99. This fraction can be used in various mathematical calculations and applications.
