Which of the following percentages is equivalent to the fraction below? 16/128
a. $12.5 \%$
c. $0.125 \%$
b. $1.25 \%$
d. $25 \%$
Answer (1)
Simplify the fraction: 128 16 = 8 1 .
Convert the fraction to a decimal: 8 1 = 0.125 .
Convert the decimal to a percentage: 0.125 × 100 = 12.5% .
The equivalent percentage is 12.5% .
Explanation
Understanding the problem We are given the fraction 128 16 and asked to find the equivalent percentage from the given options.
Simplifying the fraction First, we simplify the fraction 128 16 . Both the numerator and denominator are divisible by 16. Dividing both by 16, we get: 128 16 = 128 ÷ 16 16 ÷ 16 = 8 1
Converting to decimal Next, we convert the simplified fraction 8 1 to a decimal by dividing the numerator by the denominator: 8 1 = 0.125
Converting to percentage Now, we convert the decimal 0.125 to a percentage by multiplying it by 100: 0.125 × 100 = 12.5 So, the fraction 128 16 is equivalent to 12.5% .
Finding the matching percentage Comparing the calculated percentage with the given options, we find that option a, 12.5% , matches our result.
Examples
In everyday life, understanding percentages helps us calculate discounts while shopping. For instance, if an item originally priced at $128 is on sale with a 16 d i sco u n t , w ec an e x p ress t h e d i sco u n t a s a f r a c t i o n \frac{16}{128}$. Converting this fraction to a percentage, 12.5% , tells us the proportion of the original price that we are saving. This makes it easier to compare deals and make informed purchasing decisions.
