To determine where the number \( \frac{58}{10} \) (or 5.8) lies on a number line, we first simplify the fraction:
\[ \frac{58}{10} = 5.8 \]
Next, let's identify the range of whole numbers between which \( 5.8 \) falls. The whole numbers surrounding \( 5.8 \) are \( 5 \) and \( 6 \).
Now, we'll find out which of the provided intervals includes \( 5.8 \) when considering rational numbers to the nearest half:
- Between 8.5 and 9: This range does not include \( 5.8 \).
- Between 8 and 8.5: This range does not include \( 5.8 \).
- Between 7.5 and 8: This range does not include \( 5.8 \).
- Between 7 and 7.5: This range does not include \( 5.8 \).
Since none of the options presented are correct, it might be necessary to confirm or clarify the original question about the number \( \frac{58}{10} \) (5.8). It correctly lies between the whole numbers \( 5 \) and \( 6 \).
However, if we consider this with the intervals given, the correct answer for the rational number closest to \( 5.8 \) to the nearest half would actually be between \( 5.5 \) and \( 6 \), which is not one of the provided options.
For clarity:
- \( 5.8 \) lies between \( 5 \) and \( 6 \).
- The option closest to them should include \( 5.5 \) to \( 6 \), which is missing. Please check the original question.
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