Answer :
Sure, let's find the relative error of the measurement.
1. Step 1: Identify the given values.
- Actual length of the rug: [tex]\(34 \, \text{in}\)[/tex]
- Absolute error: [tex]\(1 \, \text{in}\)[/tex] (Option B indicates this as the absolute error)
2. Step 2: Understand relative error and how to calculate it.
- Relative error is a measure of the uncertainty of measurement relative to the size of the measurement.
- The formula for relative error (as a percentage) is given by:
[tex]\[ \text{Relative error} = \left( \frac{\text{Absolute error}}{\text{Actual measurement}} \right) \times 100 \][/tex]
3. Step 3: Substitute the given values into the formula.
- Absolute error = [tex]\(1 \, \text{in}\)[/tex]
- Actual measurement = [tex]\(34 \, \text{in}\)[/tex]
Plug these values into the formula:
[tex]\[ \text{Relative error} = \left( \frac{1}{34} \right) \times 100 \][/tex]
5. Step 4: Simplify the expression.
[tex]\[ \text{Relative error} = \left( \frac{1}{34} \right) \times 100 \approx 2.941176470588235 \][/tex]
6. Step 5: Interpret the result.
- So the relative error is approximately [tex]\(2.94\% \)[/tex].
Given the options, the one closest to our calculated relative error is Option D, which is approximately [tex]\(2 \%\)[/tex].
Therefore, the relative error of measuring the rug is closest to:
(D) [tex]\(\approx 2 \%\)[/tex]
1. Step 1: Identify the given values.
- Actual length of the rug: [tex]\(34 \, \text{in}\)[/tex]
- Absolute error: [tex]\(1 \, \text{in}\)[/tex] (Option B indicates this as the absolute error)
2. Step 2: Understand relative error and how to calculate it.
- Relative error is a measure of the uncertainty of measurement relative to the size of the measurement.
- The formula for relative error (as a percentage) is given by:
[tex]\[ \text{Relative error} = \left( \frac{\text{Absolute error}}{\text{Actual measurement}} \right) \times 100 \][/tex]
3. Step 3: Substitute the given values into the formula.
- Absolute error = [tex]\(1 \, \text{in}\)[/tex]
- Actual measurement = [tex]\(34 \, \text{in}\)[/tex]
Plug these values into the formula:
[tex]\[ \text{Relative error} = \left( \frac{1}{34} \right) \times 100 \][/tex]
5. Step 4: Simplify the expression.
[tex]\[ \text{Relative error} = \left( \frac{1}{34} \right) \times 100 \approx 2.941176470588235 \][/tex]
6. Step 5: Interpret the result.
- So the relative error is approximately [tex]\(2.94\% \)[/tex].
Given the options, the one closest to our calculated relative error is Option D, which is approximately [tex]\(2 \%\)[/tex].
Therefore, the relative error of measuring the rug is closest to:
(D) [tex]\(\approx 2 \%\)[/tex]
