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Answer :
Let's determine which of the numbers [tex]\( 57.6 \)[/tex], [tex]\( 57 \frac{1}{2} \)[/tex], [tex]\( 57.07 \)[/tex], and [tex]\( 57 \frac{2}{5} \)[/tex] is closest to 58.
1. Convert fractions to decimals:
- [tex]\( 57 \frac{1}{2} = 57 + \frac{1}{2} = 57.5 \)[/tex]
- [tex]\( 57 \frac{2}{5} = 57 + \frac{2}{5} = 57.4 \)[/tex]
2. Calculate the distance of each number from 58:
- For [tex]\( 57.6 \)[/tex], the difference is [tex]\( |58 - 57.6| = 0.4 \)[/tex]
- For [tex]\( 57.5 \)[/tex], the difference is [tex]\( |58 - 57.5| = 0.5 \)[/tex]
- For [tex]\( 57.07 \)[/tex], the difference is [tex]\( |58 - 57.07| = 0.93 \)[/tex]
- For [tex]\( 57.4 \)[/tex], the difference is [tex]\( |58 - 57.4| = 0.6 \)[/tex]
3. Compare the differences:
- [tex]\( 57.6 \)[/tex] is 0.4 away from 58.
- [tex]\( 57.5 \)[/tex] is 0.5 away from 58.
- [tex]\( 57.07 \)[/tex] is 0.93 away from 58.
- [tex]\( 57.4 \)[/tex] is 0.6 away from 58.
4. Conclusion:
The number with the smallest difference from 58 is [tex]\( 57.6 \)[/tex], which is 0.4 away.
Therefore, the number that is located closest to 58 is [tex]\( 57.6 \)[/tex]. The correct answer is option B.
1. Convert fractions to decimals:
- [tex]\( 57 \frac{1}{2} = 57 + \frac{1}{2} = 57.5 \)[/tex]
- [tex]\( 57 \frac{2}{5} = 57 + \frac{2}{5} = 57.4 \)[/tex]
2. Calculate the distance of each number from 58:
- For [tex]\( 57.6 \)[/tex], the difference is [tex]\( |58 - 57.6| = 0.4 \)[/tex]
- For [tex]\( 57.5 \)[/tex], the difference is [tex]\( |58 - 57.5| = 0.5 \)[/tex]
- For [tex]\( 57.07 \)[/tex], the difference is [tex]\( |58 - 57.07| = 0.93 \)[/tex]
- For [tex]\( 57.4 \)[/tex], the difference is [tex]\( |58 - 57.4| = 0.6 \)[/tex]
3. Compare the differences:
- [tex]\( 57.6 \)[/tex] is 0.4 away from 58.
- [tex]\( 57.5 \)[/tex] is 0.5 away from 58.
- [tex]\( 57.07 \)[/tex] is 0.93 away from 58.
- [tex]\( 57.4 \)[/tex] is 0.6 away from 58.
4. Conclusion:
The number with the smallest difference from 58 is [tex]\( 57.6 \)[/tex], which is 0.4 away.
Therefore, the number that is located closest to 58 is [tex]\( 57.6 \)[/tex]. The correct answer is option B.
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