0.51 Repeating as a Fraction
In this article, we will explore how to convert the repeating decimal 0.51 to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.51, the digits 51 repeat indefinitely, making it a repeating decimal.
Converting 0.51 to a Fraction
To convert 0.51 to a fraction, we can use the following steps:
- Let x = 0.51 We start by letting x equal 0.51.
- Multiply both sides by 100 We multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 51.51
- Subtract x from both sides We subtract x from both sides of the equation to get:
99x = 51
- Divide both sides by 99 Finally, we 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 denominator by their greatest common divisor (GCD). The GCD of 51 and 99 is 3.
x = (51 ÷ 3) / (99 ÷ 3) x = 17/33
Therefore, 0.51 repeating as a fraction is 17/33.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.51 to a fraction. The fraction equivalent of 0.51 is 17/33. This process can be applied to convert any repeating decimal to a fraction.
