Question
if a repeating decimals has a repeating cycle of three digest it will convert to a rational number with what denominotor
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GPT-4o mini
A repeating decimal with a repeating cycle of three digits can be converted into a rational number, specifically with a denominator that is a power of 10 minus 1. For a repeating decimal with a cycle of three digits, the denominator will be \(999\).
For example, if you have a repeating decimal like \(0.abcabcabc...\), you can express it as:
\[
\frac{abc}{999}
\]
where \(abc\) represents the three-digit repeating portion. So, the denominator of the rational form of a repeating decimal with a repetition of three digits is always \(999\).
For example, if you have a repeating decimal like \(0.abcabcabc...\), you can express it as:
\[
\frac{abc}{999}
\]
where \(abc\) represents the three-digit repeating portion. So, the denominator of the rational form of a repeating decimal with a repetition of three digits is always \(999\).
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