Final answer:
A sequence in the decimal expansion of a fraction is about to be repeated when the same remainder is encountered again during the division process. This is because the same remainder will yield the same quotient, thus leading to the repeating decimal.
Step-by-step explanation:
Chelsea can be sure that a sequence in her decimal expansion is about to be repeated when she gets a remainder that she has already obtained before during her division process. In mathematical terms, this is option d) When a remainder is zero. When converting a fraction into a decimal by dividing the numerator by the denominator, the decimal starts repeating when we encounter a situation in which the remainder repeats itself. At this point, since we're performing the same division, the quotient will also repeat, leading to a repeating decimal.
For example, if we are converting the fraction 1/3 into a decimal, we start dividing 1 by 3. We first get a remainder of 1. When we carry this process on, the remainder keeps repeating itself and so does the quotient (0.333...).
However, if the remainder is zero, it means the decimal has ended and it does not repeat.
Learn more about Repeat Sequences in Decimal Expansion