The Correct Answer and Explanation is:
The correct answer is 90.91%.
Converting a fraction like 20/22 into a percentage is a process of changing its format to represent a portion out of one hundred. This conversion involves a few clear steps that make the relationship between the numbers easy to understand.
The first step, while not strictly necessary but often helpful, is to simplify the fraction. To simplify 20/22, we find the largest number that can divide both the numerator (20) and the denominator (22) without a remainder. This number is 2. When we divide both parts of the fraction by 2, we get 10/11. This simplified fraction is equivalent to the original and is often easier to work with in calculations.
The second step is to convert this fraction into a decimal. A fraction is simply another way of writing a division problem. So, to get the decimal, we divide the numerator by the denominator. In this case, we perform the division 10 ÷ 11. This calculation results in a repeating decimal, which is 0.909090… The pattern of “90” continues infinitely. This decimal value represents the same proportion as the fraction 10/11.
The third and final step is to convert the decimal into a percentage. The word “percent” means “per hundred,” so to make this conversion, we multiply the decimal value by 100. Multiplying 0.909090… by 100 shifts the decimal point two places to the right, giving us 90.9090… We then add the percent symbol (%) to indicate the new format.
Because the decimal repeats, it is practical to round the number to a standard number of decimal places for everyday use. Rounding to two decimal places is common. To do this, we look at the third decimal digit, which is 9. Since this digit is 5 or greater, we round up the preceding digit. Therefore, 90.90% becomes 90.91%.
