To determine which whole number and rational number to the nearest half the number 105 falls between, we need to look at the whole number part first, which is 105 itself.
On a number line, 105 is clearly a whole number.
Next, we need to find the rational number to the nearest half. The nearest half to 105 is 105.0.
Now, let's examine the provided options:
- between 10 and 10.5
- between 9.5 and 10
- between 10.5 and 11
- between 11 and 11.5
None of these options apply to the number 105.
However, if the question was intended to refer to a number around 10 (which seems highly unlikely considering the clear context), the reasonable number pairings would be more like surrounding 10 or in the context of 105 itself would be different.
Therefore, the choices themselves likely are not associated correctly with 105, so none of the options correctly represents a range that includes 105.