0.72 Repeating as a Simplified Fraction
What is 0.72 Repeating?
0.72 repeating, also known as 0.72~, is a decimal number that has a repeating pattern of 2's after the decimal point. In other words, it can be written as 0.722222... where the 2's go on indefinitely.
Converting 0.72 Repeating to a Fraction
To convert 0.72 repeating to a simplified fraction, we can use a few different methods. One way is to use the fact that a repeating decimal can be converted to a fraction by using the following formula:
x = a / (10^n - 1)
where x is the repeating decimal, a is the number of decimal places in the repeating part, and n is the number of digits in the repeating part.
In this case, x = 0.72~, a = 2, and n = 2. Plugging these values into the formula, we get:
0.72~ = 2 / (10^2 - 1) 0.72~ = 2 / 99 0.72~ = 2/99
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2 and 99 is 1, so the fraction is already in its simplest form.
Final Answer
Therefore, 0.72 repeating as a simplified fraction is 2/99.
Conclusion
In this article, we have converted 0.72 repeating to a simplified fraction using the formula for converting repeating decimals to fractions. We have also simplified the fraction to its simplest form, resulting in the final answer of 2/99.
