.51 Repeating as a Fraction
The decimal number .51 repeating is a fascinating mathematical concept that can be expressed as a fraction. In this article, we'll explore how to convert .51 repeating to a fraction and understand its equivalent value.
What is .51 Repeating?
.51 repeating, also written as 0.51¯, is a decimal number where the digits "51" repeat indefinitely. This means that the decimal expansion goes on forever, with the same two digits repeating in a cycle:
0.51 51 51 51 ...
Converting .51 Repeating to a Fraction
To convert .51 repeating to a fraction, we can use a simple method. Let's define the repeating decimal as x:
x = 0.51¯
Since the decimal repeats every two digits, we can multiply both sides of the equation by 100:
100x = 51.51¯
Subtracting x from both sides gives us:
99x = 51
Now, we can divide both sides by 99 to solve for x:
x = 51/99
So, .51 repeating is equal to the fraction 51/99.
Simplifying the Fraction
We can simplify the fraction 51/99 by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 51 and 99 is 3. Therefore, we can simplify the fraction as:
x = (51 ÷ 3) / (99 ÷ 3) = 17/33
So, .51 repeating is equal to the simplified fraction 17/33.
Conclusion
In conclusion, .51 repeating can be expressed as a fraction, specifically 51/99 or its simplified form 17/33. Understanding how to convert repeating decimals to fractions is an essential skill in mathematics, and this example demonstrates a simple method for doing so.
