To determine the whole number and the rational number to the nearest half that 105 falls between, we need to analyze the value of 105 in relation to these options.
Since the number 105 does not fall between any of the provided ranges of decimal fractions near whole numbers, we should clarify what is being asked with respect to whole numbers around 105.
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The whole number immediately less than 105 is 104, and the whole number immediately greater than 105 is 106.
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As for halves, we can look at the nearest halves surrounding 105:
- 105 can also be approximated in relation to halves which precede and follow it. Specifically, the nearest half less than 105 is 104.5, and the nearest half greater than is 105.5.
Given all factors of analysis for the specified choices, the whole number that 105 falls between is 104 and 106, while the rational number to the nearest half is 105 itself.
Given the choices for placement on a number line, however, below is a detailed evaluation of options:
- between 9.5 and 10
- between 10.5 and 11
- between 11 and 11.5
- between 10 and 10.5
None of the choices are relevant, since 105 is not within the provided ranges. Therefore, there may be a misunderstanding or oversight in the question's stated parameters.
If assistance needed is strictly with the default numbers: 105 does not belong to any of these specified intervals. However, indicated the correct notion of wholes numbers relative to rational numbers would yield “between 104 and 106” and focusing on halves as “105” returning as an answer.