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
Simplifying the Fraction First, we need to simplify the fraction 128 16 . Both the numerator and the 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. To do this, we divide the numerator (1) by the denominator (8): 8 1 = 1 ÷ 8 = 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 Answer Comparing our result with the given options, we find that option a, 12.5% , is the correct answer.
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% discount, you can calculate the discount amount by finding 16/128 (which simplifies to 1/8 or 12.5%) of the original price. This means you're saving 12.5% of the original price, helping you make informed purchasing decisions and manage your budget effectively. This skill is crucial for making smart financial choices and understanding value.
