Question

demetrius says that because percent means \out of 100,\ he needs to multiply 3.7 by $\frac{1}{100}$ to write a percentage that is equivalent to 3.7.
help demetrius understand his mistake.

Explanation:

Percent means "out of 100", so to convert a number greater than 1 to a percentage, you multiply by 100 (not $\frac{1}{100}$) to show how many parts out of 100 it represents. Multiplying by $\frac{1}{100}$ would shrink the number, which is for converting a percentage to a decimal, not the reverse.

Answer:

Demetrius has the operation backwards. To convert 3.7 to a percentage, he needs to multiply by 100 (not $\frac{1}{100}$), since percent represents a value relative to 100. $3.7 \times 100 = 370\%$, which is the correct percentage equivalent of 3.7. Multiplying by $\frac{1}{100}$ would convert a percentage to a decimal, not the other way around.