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Answer :
To find which number is closest to -77, we can compare the absolute differences between each option and -77. Let's break down each option one by one:
1. Option A: 76.3
- Calculate the difference:
[tex]\[
|76.3 - (-77)| = |76.3 + 77| = 153.3
\][/tex]
- This shows that 76.3 is quite far from -77.
2. Option B: -76.25
- Calculate the difference:
[tex]\[
|-76.25 - (-77)| = |-76.25 + 77| = |0.75|
\][/tex]
- This is a small difference, indicating that -76.25 is quite close to -77.
3. Option C: [tex]\(-76 \frac{3}{5}\)[/tex]
- First, convert the fraction into a decimal:
[tex]\[
-76 \frac{3}{5} = -76 + 0.6 = -76.6
\][/tex]
- Calculate the difference:
[tex]\[
|-76.6 - (-77)| = |-76.6 + 77| = |0.4|
\][/tex]
- This has a larger difference compared to -76.25.
4. Option D: [tex]\(-76 \frac{1}{10}\)[/tex]
- Convert the fraction into a decimal:
[tex]\[
-76 \frac{1}{10} = -76 + 0.1 = -76.1
\][/tex]
- Calculate the difference:
[tex]\[
|-76.1 - (-77)| = |-76.1 + 77| = |0.9|
\][/tex]
- This is further away than -76.25 and -76.6.
After comparing the differences, the smallest absolute difference is for Option B, [tex]\(-76.25\)[/tex], with a difference of [tex]\(0.75\)[/tex]. Therefore, the number closest to -77 is B: -76.25.
1. Option A: 76.3
- Calculate the difference:
[tex]\[
|76.3 - (-77)| = |76.3 + 77| = 153.3
\][/tex]
- This shows that 76.3 is quite far from -77.
2. Option B: -76.25
- Calculate the difference:
[tex]\[
|-76.25 - (-77)| = |-76.25 + 77| = |0.75|
\][/tex]
- This is a small difference, indicating that -76.25 is quite close to -77.
3. Option C: [tex]\(-76 \frac{3}{5}\)[/tex]
- First, convert the fraction into a decimal:
[tex]\[
-76 \frac{3}{5} = -76 + 0.6 = -76.6
\][/tex]
- Calculate the difference:
[tex]\[
|-76.6 - (-77)| = |-76.6 + 77| = |0.4|
\][/tex]
- This has a larger difference compared to -76.25.
4. Option D: [tex]\(-76 \frac{1}{10}\)[/tex]
- Convert the fraction into a decimal:
[tex]\[
-76 \frac{1}{10} = -76 + 0.1 = -76.1
\][/tex]
- Calculate the difference:
[tex]\[
|-76.1 - (-77)| = |-76.1 + 77| = |0.9|
\][/tex]
- This is further away than -76.25 and -76.6.
After comparing the differences, the smallest absolute difference is for Option B, [tex]\(-76.25\)[/tex], with a difference of [tex]\(0.75\)[/tex]. Therefore, the number closest to -77 is B: -76.25.
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