How many positive integers less than 100 have reciprocals with terminating decimal representation?

Answer 1

To determine how many positive integers less than 100 have reciprocals with terminating decimal representation, we need to consider the prime factorization of each integer. Any positive integer whose prime factorization consists only of 2s and/or 5s will have a reciprocal with a terminating decimal representation. In the range of positive integers less than 100, there are 49 numbers that are powers of 2, 5, or their products (2^0, 2^1, 2^2, ..., 2^6, 5^0, 5^1, 5^2). Therefore, there are 49 positive integers less than 100 with reciprocals having terminating decimal representations.

Answer 2

Well, honey, let me break it down for you. The positive integers with reciprocals that have a terminating decimal representation are the ones that only have 2 and 5 as prime factors in their denominator. So, you just need to count how many numbers less than 100 can be expressed as 2^a * 5^b where a and b are non-negative integers. And the answer is 40.

Answer 3

Oh, dude, this is like a math riddle or something. So, you know how reciprocals with terminating decimal representations are like 1/2 or 1/4, right? Well, those are like fractions with powers of 2 in the denominator. So, you just gotta count how many positive integers less than 100 have only 2s and 5s in their prime factorization. I mean, it's not rocket science, but it's kinda fun to figure out.

Answer 4

There are 14.

Answer 5

13

Answer 6

14