Final answer:
To find the number of integers between $(10.2)^3$ and $(10.3)^3$, calculate the difference and round up to the nearest whole number, resulting in 1 integer.
Step-by-step explanation:
To find the number of integers between $(10.2)^3$ and $(10.3)^3$, we need to find the difference between the two numbers and then round it up to the nearest whole number.
The difference between $(10.2)^3$ and $(10.3)^3$ is $(10.3)^3 - (10.2)^3 = 1.0$. Rounding up 1.0 to the nearest whole number gives us 1.
Therefore, there is 1 integer between $(10.2)^3$ and $(10.3)^3$.