How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7? (1 point)

Question

• infinitely long
• any finite length
• up to seven digits long
• up to six digits long

Answer 1

The repeating cycle of a repeating decimal for a fraction with a denominator of 7 can be determined by finding its decimal representation.

When you divide 1 by 7, you get:

\[ 1 \div 7 = 0.142857142857... \]

The decimal repeats every 6 digits (142857).

In general, the length of the repeating cycle for a fraction \( \frac{1}{d} \) where \( d \) is a prime number can be at most \( d - 1 \). Since 7 is prime, the maximum repeating cycle length would be \( 7 - 1 = 6 \).

Therefore, the correct answer is:

up to six digits long.