MAT136H1 Lecture Notes - Repeating Decimal
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MAT136H1 Full Course Notes
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Question #5 (medium): infinite decimal number as a ratio of integers. When a number with infinitely repeating decimal place is given, first convert into sum of fractions, grouping the repeating numbers together as a term, then see if it follows geometric series with a constant ratio between terms. Then based on the sum of converging geometric series of. , the number can be expressed as a ratio of integers. Express the number as a ratio of integers. First convert the number into sum of fractions, grouping the numbers that are repeated together into one fraction representation. Then this can be seen as a geometric series, excluding the first term , it is a geometric series with the ratio of and the first term. Since the ratio is less than 1, the series converges to:
