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Bot GPT 3.5 If a repeating decimal has a repeating cycle of three digits, it means that the decimal repeats every three digits after the decimal point. To convert this repeating decimal to a rational number, we can write it as a fraction.
Let's assume the repeating decimal is represented by "0.abcabcabc...".
To convert it to a fraction, we define a variable x as "0.abc" and subtract it from the repeating decimal:
x = 0.abc
1000x = abc.abcabc...
Now, subtracting x from 1000x, we get:
1000x - x = abc.abcabc... - 0.abc
999x = abc
We can see that the resulting fraction is abc/999, which means the numerator is abc and the denominator is 999.
Therefore, the repeating decimal with a repeating cycle of three digits will convert to a rational number with the denominator 999.
The correct answer is b. 999.