Question

For each of the following pairs of numbers, find a decimal between the two numbers

a) The numbers 2.981 and 2.982
b) The numbers 13 and 12.9999
c) The numbers 13 and 13.0001
d) none of the above

Answer 1

Decimals between the numbers 2.981 and 2.982 can be 2.9815, between 13 and 12.9999 there are effectively no decimals as they are equal when rounded, and between 13 and 13.0001 can be 13.00005.

Step-by-step explanation:

For each of the following pairs of numbers, to find a decimal between the two numbers, choose a value that is greater than the first number and less than the second number.

1. The numbers 2.981 and 2.982: A decimal between these two numbers could be 2.9815. This number is greater than 2.981 and less than 2.982.
2. The numbers 13 and 12.9999: Although 13 is greater than 12.9999, there is no decimal number between these two since 12.9999 essentially rounds up to 13. A possible alternative could be 12.99995, but the correct answer in this context is that there isn't a number between 13 and 12.9999 because they are equal when rounding to four decimal places.
3. The numbers 13 and 13.0001: A decimal that lies between these numbers is 13.00005. It is greater than 13 and less than 13.0001.
4. None of the above: This is not a valid choice since we have found decimals between the pairs given in options a and c.

For the other examples provided, the concept of expressing numbers in scientific notation and using the proper number of significant figures is distinct from finding decimals between numbers, yet both involve a deep understanding of numerical representation and precision.