.05 Repeating as a Fraction
In mathematics, a fraction is a way to represent a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). Fractions can be used to represent decimals, including repeating decimals like .05.
What is .05 Repeating?
.05 repeating, also written as .050505..., is a decimal that has a repeating pattern of 05. This means that the sequence of 05 will continue indefinitely.
Converting .05 Repeating to a Fraction
To convert .05 repeating to a fraction, we can use a simple trick. We can multiply the decimal by a power of 10, and then subtract the original decimal to get an equation with the repeating part on one side and a whole number on the other.
Let's do this with .05 repeating:
Step 1: Multiply by 100
100 × .050505... = 5.050505...
Step 2: Subtract the original decimal
5.050505... - .050505... = 5
This gives us the equation:
100x - x = 5
where x is the decimal .050505....
Step 3: Simplify the equation
99x = 5
Step 4: Divide by 99
x = 5/99
So, .05 repeating as a fraction is equal to:
5/99
This fraction is a simplified form of the repeating decimal .05.
Conclusion
In conclusion, .05 repeating can be converted to a fraction by using a simple trick involving multiplication and subtraction. The resulting fraction is 5/99, which is a simplified form of the repeating decimal.
