0.081 Recurring as a Fraction
What is 0.081 Recurring?
0.081 recurring, also known as 0.081~, is a decimal number that has a repeating pattern of digits. In this case, the digits "081" repeat indefinitely. This type of number is known as a recurring decimal or a repeating decimal.
Converting 0.081 Recurring to a Fraction
To convert 0.081 recurring to a fraction, we can use a few different methods. One way is to use the formula:
x = 0.081~
Multiplying both sides by 1000 (since there are 3 repeating digits), we get:
1000x = 81.081~
Subtracting the original equation from this new equation, we get:
999x = 81
Dividing both sides by 999, we get:
x = 81/999
Simplifying the Fraction
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 81 and 999 is 81, so we can divide both numbers by 81:
x = (81 ÷ 81) / (999 ÷ 81)
x = 1/11
Therefore, 0.081 recurring as a fraction is equal to 1/11.
Conclusion
In conclusion, we have successfully converted 0.081 recurring to a fraction, which is equal to 1/11. This conversion can be useful in various mathematical applications, such as algebra and geometry.
