0.518 Repeating as a Fraction
What is 0.518 Repeating?
0.518 repeating is a decimal number that has a repeating pattern of digits. In this case, the pattern is 518, which repeats indefinitely: 0.518۱۸۱۸۱۸... . This type of number is also known as a repeating decimal or a non-terminating decimal.
Converting 0.518 Repeating to a Fraction
To convert 0.518 repeating to a fraction, we need to find the equivalent fraction that represents the same value. There are a few ways to do this, but one common method is to use the following formula:
x = 0.518۱۸۱۸۱۸... (10^2)x = 51.۸۱۸۱۸۱۸...
By multiplying both sides of the equation by 10^2 (100), we can eliminate the decimal point and create a new equation:
100x = 51.۸۱۸۱۸۱۸...
Next, we can subtract the original equation from this new equation to get:
99x = 51
Now, we can divide both sides of the equation by 99 to solve for x:
x = 51/99
Simplifying the Fraction
The fraction 51/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 51 and 99 is 3, so we can divide both numbers by 3:
x = (51 ÷ 3) / (99 ÷ 3) x = 17/33
Therefore, the fraction equivalent to 0.518 repeating is 17/33.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.518 to a fraction, which is 17/33. This process can be applied to any repeating decimal, and it is an important concept in mathematics, particularly in algebra and number theory.
