Question
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
100
100
99
99
999
999
1,000
1,000
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Responses
100
100
99
99
999
999
1,000
1,000
Skip to navigation
page 14 of 14
Answers
GPT-4o mini
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of **999**.
This is because the denominator used for a repeating decimal that has n digits in its repeating cycle is \(10^n - 1\). For a cycle of three digits, \(10^3 - 1 = 1000 - 1 = 999\).
This is because the denominator used for a repeating decimal that has n digits in its repeating cycle is \(10^n - 1\). For a cycle of three digits, \(10^3 - 1 = 1000 - 1 = 999\).