0.20 Repeating as a Fraction
In mathematics, repeating decimals are decimals that have a sequence of digits that repeats indefinitely. One such example is 0.20 repeating, also written as 0.2020... or 0.2¯. But what is 0.20 repeating as a fraction?
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use the following method:
Let the repeating decimal be x. Multiply both sides of the equation by 10 to the power of the number of repeating digits. For example, if the repeating decimal is 0.2020..., we multiply both sides by 100 (10^2).
100x = 20.2020...
Next, subtract the original equation from the new equation to eliminate the repeating decimal part.
100x - x = 20.2020 - 0.2020
99x = 20
Now, divide both sides of the equation by the coefficient of x (in this case, 99).
x = 20/99
0.20 Repeating as a Fraction
Using the method above, we can convert 0.20 repeating to a fraction.
Let x = 0.2020...
Multiply both sides by 100:
100x = 20.2020...
Subtract the original equation from the new equation:
100x - x = 20.2020 - 0.2020
99x = 20
Divide both sides by 99:
x = 20/99
Therefore, 0.20 repeating as a fraction is 20/99.
Conclusion
In conclusion, we have successfully converted 0.20 repeating to a fraction using the method of multiplying by 10 to the power of the number of repeating digits, subtracting the original equation, and dividing by the coefficient of x. The resulting fraction is 20/99.
