What is 8.8 percent as a fraction in simplest form
The Correct Answer and Explanation is:
To convert 8.8% to a fraction in simplest form, start by understanding that a percentage is simply a fraction out of 100. So, 8.8% can be written as:
[
\frac{8.8}{100}
]
However, to eliminate the decimal, multiply both the numerator and the denominator by 10:
[
\frac{8.8 \times 10}{100 \times 10} = \frac{88}{1000}
]
Now, simplify (\frac{88}{1000}) by finding the greatest common divisor (GCD) of 88 and 1000, which is 8:
[
\frac{88 \div 8}{1000 \div 8} = \frac{11}{125}
]
So, 8.8% as a fraction in simplest form is (\frac{11}{125}).
Explanation
Percentages are ways to express ratios as parts per hundred, which means “percent” literally translates to “per hundred.” Converting a percentage to a fraction involves expressing the percentage as a fraction over 100, which provides an easy way to compare and simplify ratios. Here, 8.8% starts as (\frac{8.8}{100}), but fractions with decimals are typically converted into whole numbers for easier simplification. By multiplying both the numerator and the denominator by 10, we eliminate the decimal.
Once we get (\frac{88}{1000}), simplifying the fraction requires finding the GCD. This is an essential step because it reduces the fraction to its simplest form, making it easier to interpret and use in mathematical calculations. By dividing both the numerator and denominator by their GCD, 8, we get the simplest form, (\frac{11}{125}), which is fully reduced and cannot be simplified further.
In summary, converting 8.8% to a fraction in simplest form involves expressing it over 100, removing decimals, and simplifying. This approach works for any percentage and ensures the final answer is as clear and usable as possible.