if a repeating decimals has a repeating cycle of three digest it will convert to a rational number with what denominotor

Answer 1

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 \(999\).