0.2 Repeating Decimal as a Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One example of a repeating decimal is 0.2, where the digit 2 repeats indefinitely. But have you ever wondered how to express 0.2 as a fraction?
Converting 0.2 to a Fraction
To convert 0.2 to a fraction, we need to find the equivalent fraction that has the same value as the repeating decimal. One way to do this is to use the following formula:
x = 0.2 (1) 10x = 2.2 (2)
First, we multiply equation (1) by 10 to get equation (2). Then, we subtract equation (1) from equation (2) to eliminate the repeating decimal:
10x - x = 2.2 - 0.2 9x = 2 x = 2/9
Therefore, the fraction equivalent to 0.2 is 2/9.
Verifying the Result
To verify that 2/9 is indeed the correct fraction, we can convert it back to a decimal:
2/9 = 0.222...
As you can see, the fraction 2/9 equals the repeating decimal 0.2. This confirms that we have successfully converted 0.2 to a fraction.
Conclusion
In conclusion, the repeating decimal 0.2 can be expressed as a fraction, specifically 2/9. This conversion can be done using the method shown above, and the result can be verified by converting the fraction back to a decimal. Understanding how to convert repeating decimals to fractions is an important concept in mathematics and can be applied to a wide range of problems.
