In a fraction with the denominator of 15, which value could the numerator be to produce a repeating decimal?
a) 15
b) 9
c) 11
d) 12
all fractions whose denominator (in lowest terms) contains only powers of 2 and 5 terminate.
Any other factor in the bottom produces a repeating decimal.
So, your numerator can be anything that does not have a factor of 3 to cancel the 3 in 15.
Divide the numerator by the denominator.
I'll be glad to check your answer.
15
To find the answer, we need to understand the relationship between the numerator and denominator in a fraction in order to produce a repeating decimal.
The numerator of a fraction represents a whole number and the denominator represents how many equal parts the whole is divided into.
In order for a fraction to produce a repeating decimal, the denominator must have a prime factor other than 2 or 5.
Now, let's consider the options:
a) If the numerator is 15, then the fraction is 15/15, which simplifies to 1. This is not a repeating decimal.
b) If the numerator is 9, then the fraction is 9/15. To check if this produces a repeating decimal, we need to factor the denominator, which is 15. The factors of 15 are 3 and 5. Since 3 is a prime factor other than 2 or 5, this fraction will produce a repeating decimal.
c) If the numerator is 11, then the fraction is 11/15. Factoring the denominator, we get 3 and 5. Since 3 is a prime factor other than 2 or 5, this fraction will produce a repeating decimal.
d) If the numerator is 12, then the fraction is 12/15. Factoring the denominator, we get 3 and 5. Since 3 is a prime factor other than 2 or 5, this fraction will produce a repeating decimal.
So, the values of the numerators that could produce a fraction with a repeating decimal for a denominator of 15 are b) 9, c) 11, and d) 12.