Question

Maria rewrites a fraction less than 1as a decimal. The numerator is a whole number greater than 0. For which denominator will the fraction always convert to a repeating decimal?

Answer 1

answer choices (please post these next time)

6, 11, 15, or 18

Answer 2

this is kind of hard to explain, but I'll try:

the denominator you're looking for (one that always converts the fraction to a repeating decimal) you should look for a prime number

I'll use 6 as an example, and demonstrate why it's wrong:

let's start by listing fractions, less than 1, with 6 as a denominator:

1/6, 2/6, 3/6, 4/6, 5/6

converting these to decimals, notice how 1/6 and 2/6 are repeating decimals (0.66repeated, and 0.33repeated). however, once you get to 3/6 this converts to 1/2, which is non-repeating. this happens because 3 is a factor of 6. therefore,

\[\frac{ 3 }{ 6 }=\frac{ 3 }{ 3*2}\]
the 3 cancels out in the numerator and denominator because it's a common factor, leaving 1 in the numerator and another integer in the denominator. in this case, the remaining 2 in the denominator causes the fraction to become a terminating decimal.

Answer 3

apologies if this is long-winded, but in short look between 11, 15, and 18 to see which one is prime

Answer 4

*sorry, typo, 1/6 = 0.166repeated, not 0.66 repeated