0.022 Repeating as a Fraction
The decimal number 0.022 with a repeating pattern is a fascinating concept in mathematics. In this article, we will explore how to convert this repeating decimal into a fraction.
Repeating Decimals
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.022 is a repeating decimal because the sequence "022" repeats forever. This type of decimal is also known as a non-terminating decimal.
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use the following formula:
x = d/d
where x is the repeating decimal and d is the number of digits in the repeating pattern.
Converting 0.022 Repeating to a Fraction
Let's apply the formula to convert 0.022 repeating to a fraction.
x = 0.022 d = 3 (because the repeating pattern is "022" which has 3 digits)
Now, let's plug in the values into the formula:
x = d/d 0.022 = 2/90
Simplifying the fraction, we get:
0.022 = 1/45
Therefore, the fraction equivalent of 0.022 repeating is 1/45.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.022 to a fraction using the formula x = d/d. The resulting fraction is 1/45, which is a simple and elegant representation of the original decimal number. This process can be applied to any repeating decimal to convert it into a fraction.
