How many natural numbers lie between 7.001 and 47.999?

Answer: 40

Step-by-step solution

Step 1: Identify natural numbers and find the smallest natural number

Natural numbers are the positive counting integers: $1, 2, 3, \dots$ . For a natural number to lie between $7.001$ and $47.999$ , it must be strictly greater than $7.001$ and strictly less than $47.999$ . The smallest integer strictly greater than $7.001$ is $8$ .

Step 2: Find the largest natural number

Next, we find the upper bound for our natural numbers. The largest integer strictly less than $47.999$ is $47$ . Therefore, the set of natural numbers lying in the given range is from $8$ to $47$ inclusive.

Step 3: Count the total number of natural numbers

To find how many integers there are from $8$ through $47$ inclusive, we subtract the lower endpoint from the upper endpoint and add $1$ : $47 - 8 + 1 = 40$ . Thus, there are $40$ natural numbers between $7.001$ and $47.999$ .

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