0.05 with a Repeating 5 as a Fraction
In this article, we will explore how to convert the decimal number 0.05 with a repeating 5 to 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 0.05 with a repeating 5, the decimal representation is 0.05555..., where the sequence "5" repeats indefinitely.
Converting a Repeating Decimal to a Fraction
To convert a repeating decimal to a fraction, we can use a simple technique. Let's denote the repeating decimal as x. We can set up two equations:
Equation 1: x = 0.05555...
Equation 2: 100x = 5.5555...
Notice that the second equation is obtained by multiplying the first equation by 100. Now, we can subtract Equation 1 from Equation 2 to eliminate the repeating decimal part:
Equation 3: 99x = 5.5 - 0.05
Equation 3: 99x = 5.45
Now, we can solve for x:
x = 5.45 / 99
x = 11 / 198
Simplifying the Fraction
We can simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 11:
x = 1 / 18
Therefore, 0.05 with a repeating 5 can be written as a fraction as 1/18.
Conclusion
In this article, we have shown how to convert a repeating decimal to a fraction. Specifically, we have converted 0.05 with a repeating 5 to the fraction 1/18. This technique can be applied to any repeating decimal to convert it to a fraction.
