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Answer :
To estimate [tex]\(68\%\)[/tex] of [tex]\(68\)[/tex], we need to find the value that is closest to this calculation based on the given options.
First, let's calculate [tex]\(68\%\)[/tex] of [tex]\(68\)[/tex] directly:
1. Convert the percentage to a decimal:
[tex]\(68\% = \frac{68}{100} = 0.68\)[/tex]
2. Multiply this decimal by 68:
[tex]\(0.68 \times 68 = 46.24\)[/tex]
Now, let's evaluate each option by calculating and comparing how close they are to [tex]\(46.24\)[/tex]:
1. Option 1: [tex]\(\frac{2}{3} \times 66\)[/tex]
Calculation: [tex]\(\frac{2}{3} \times 66 = 44.0\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 44.0| = 2.24\)[/tex]
2. Option 2: [tex]\(\frac{3}{4} \times 66\)[/tex]
Calculation: [tex]\(\frac{3}{4} \times 66 = 49.5\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 49.5| = 3.26\)[/tex]
3. Option 3: [tex]\(\frac{2}{3} \times 69\)[/tex]
Calculation: [tex]\(\frac{2}{3} \times 69 = 46.0\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 46.0| = 0.24\)[/tex]
4. Option 4: [tex]\(\frac{3}{4} \times 69\)[/tex]
Calculation: [tex]\(\frac{3}{4} \times 69 = 51.75\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 51.75| = 5.51\)[/tex]
Now, compare the differences:
- Option 1: 2.24
- Option 2: 3.26
- Option 3: 0.24
- Option 4: 5.51
The option with the smallest difference is Option 3, which has a difference of [tex]\(0.24\)[/tex]. This means that [tex]\(\frac{2}{3} \times 69\)[/tex] is the most accurate estimate for [tex]\(68\%\)[/tex] of [tex]\(68\)[/tex].
First, let's calculate [tex]\(68\%\)[/tex] of [tex]\(68\)[/tex] directly:
1. Convert the percentage to a decimal:
[tex]\(68\% = \frac{68}{100} = 0.68\)[/tex]
2. Multiply this decimal by 68:
[tex]\(0.68 \times 68 = 46.24\)[/tex]
Now, let's evaluate each option by calculating and comparing how close they are to [tex]\(46.24\)[/tex]:
1. Option 1: [tex]\(\frac{2}{3} \times 66\)[/tex]
Calculation: [tex]\(\frac{2}{3} \times 66 = 44.0\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 44.0| = 2.24\)[/tex]
2. Option 2: [tex]\(\frac{3}{4} \times 66\)[/tex]
Calculation: [tex]\(\frac{3}{4} \times 66 = 49.5\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 49.5| = 3.26\)[/tex]
3. Option 3: [tex]\(\frac{2}{3} \times 69\)[/tex]
Calculation: [tex]\(\frac{2}{3} \times 69 = 46.0\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 46.0| = 0.24\)[/tex]
4. Option 4: [tex]\(\frac{3}{4} \times 69\)[/tex]
Calculation: [tex]\(\frac{3}{4} \times 69 = 51.75\)[/tex]
Difference from 46.24: [tex]\( |46.24 - 51.75| = 5.51\)[/tex]
Now, compare the differences:
- Option 1: 2.24
- Option 2: 3.26
- Option 3: 0.24
- Option 4: 5.51
The option with the smallest difference is Option 3, which has a difference of [tex]\(0.24\)[/tex]. This means that [tex]\(\frac{2}{3} \times 69\)[/tex] is the most accurate estimate for [tex]\(68\%\)[/tex] of [tex]\(68\)[/tex].
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