Question

If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?

A) 2/11
B) 1/3
C) 41/99
D) 2/3
E) 23/37

Answer 1

To determine which fraction has the longest sequence of different digits when written as a repeating decimal, convert each fraction into decimal form. The fraction with the longest sequence of different digits is 23/37.

Step-by-step explanation:

To determine which fraction has the longest sequence of different digits when written as a repeating decimal, we need to convert each fraction into decimal form.

(A) 2/11 = 0.181818... (sequence of 2 different digits)

(B) 1/3 = 0.333... (sequence of 1 digit)

(C) 41/99 = 0.414141... (sequence of 2 different digits)

(D) 2/3 = 0.666... (sequence of 1 digit)

(E) 23/37 = 0.621621... (sequence of 3 different digits)

Therefore, the fraction with the longest sequence of different digits is 23/37.