The Correct Answer and Explanation is:
The correct answer is 16.66…% or, more precisely, 16 2/3 %.
To convert the fraction 2/12 into a percentage, you can follow a systematic, three-step process. This method ensures accuracy and helps in understanding the relationship between fractions, decimals, and percentages.
The first step is to simplify the fraction 2/12. Simplifying a fraction before performing other calculations makes the numbers smaller and easier to work with. To simplify, you find the greatest common divisor (GCD), which is the largest number that can divide both the numerator (2) and the denominator (12) without leaving a remainder. In this case, the GCD is 2. Dividing both the numerator and the denominator by 2 gives you: 2 ÷ 2 = 1, and 12 ÷ 2 = 6. Thus, the simplified fraction is 1/6.
The second step is to convert the simplified fraction into a decimal. A fraction represents a division problem, so to convert 1/6 to a decimal, you divide the numerator (1) by the denominator (6). Performing this division, 1 ÷ 6, results in a repeating decimal: 0.1666… The ellipsis indicates that the digit 6 repeats infinitely. This decimal value is the foundation for finding the final percentage.
The third and final step is to convert this decimal into a percentage. The word “percent” means “out of one hundred,” so to make this conversion, you multiply the decimal value by 100 and affix the percent symbol (%). Multiplying 0.1666… by 100 moves the decimal point two places to the right, resulting in 16.666…%. While this is a correct answer, it is often more accurate to express the repeating part as a fraction. The repeating decimal 0.666… is equivalent to the fraction 2/3. Therefore, the most precise way to state the answer is as a mixed number percentage: 16 2/3 %.
