Converting 0.16 Repeating to a Percent
Have you ever wondered how to convert a repeating decimal like 0.16 to a percent? In this article, we'll explore the steps to do just that.
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 0.16, the "16" repeats indefinitely. Repeating decimals can be converted to fractions, and then to percents.
Converting 0.16 Repeating to a Fraction
To convert 0.16 repeating to a fraction, we can use the following steps:
- Let x = 0.1616... (where the "16" repeats indefinitely)
- Multiply both sides of the equation by 100 to get 100x = 16.1616...
- Subtract the original equation from the new equation to get 99x = 16
- Divide both sides by 99 to get x = 16/99
So, 0.16 repeating is equal to the fraction 16/99.
Converting the Fraction to a Percent
To convert the fraction 16/99 to a percent, we can divide the numerator by the denominator and multiply by 100:
(16 ÷ 99) x 100 = 16.16%
Conclusion
In conclusion, 0.16 repeating is equal to 16.16%. This conversion can be useful in a variety of mathematical and real-world applications. By following the steps outlined above, you can convert any repeating decimal to a fraction and then to a percent.
