5. A metal plate is supposed to be 15.75 cm long but after it is cut, it measures 15.71 cm. Determine the relative error rounded to the nearest tenth of a percent.
5. A metal plate is supposed to be 15.75 cm long but after it is cut, it measures 15.71 cm. Determine the relative error rounded to the nearest tenth of a percent.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![### Problem Statement
A metal plate is supposed to be 15.75 cm long but after it is cut, it measures 15.71 cm. Determine the relative error rounded to the nearest tenth of a percent.
### Solution
To determine the relative error, we use the following formula:
\[ \text{Relative Error} = \left(\frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}}\right) \times 100\% \]
#### Step-by-Step Calculation
1. **Identify the measured value and the true value:**
\[
\text{True Value} = 15.75 \, \text{cm}
\]
\[
\text{Measured Value} = 15.71 \, \text{cm}
\]
2. **Calculate the absolute error:**
\[
|\text{Measured Value} - \text{True Value}| = |15.71 - 15.75| = 0.04 \, \text{cm}
\]
3. **Calculate the relative error:**
\[
\text{Relative Error} = \left(\frac{0.04}{15.75}\right) \times 100\% \approx 0.254\%
\]
4. **Round to the nearest tenth of a percent:**
\[
\text{Relative Error} \approx 0.3\%
\]
### Conclusion
The relative error, rounded to the nearest tenth of a percent, is approximately **0.3%**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8918ac98-5bcf-465f-8c11-409b4d478a84%2F40b0798b-df65-4fe7-9a3b-d08c1808cc4b%2F4g6j2zk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A metal plate is supposed to be 15.75 cm long but after it is cut, it measures 15.71 cm. Determine the relative error rounded to the nearest tenth of a percent.
### Solution
To determine the relative error, we use the following formula:
\[ \text{Relative Error} = \left(\frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}}\right) \times 100\% \]
#### Step-by-Step Calculation
1. **Identify the measured value and the true value:**
\[
\text{True Value} = 15.75 \, \text{cm}
\]
\[
\text{Measured Value} = 15.71 \, \text{cm}
\]
2. **Calculate the absolute error:**
\[
|\text{Measured Value} - \text{True Value}| = |15.71 - 15.75| = 0.04 \, \text{cm}
\]
3. **Calculate the relative error:**
\[
\text{Relative Error} = \left(\frac{0.04}{15.75}\right) \times 100\% \approx 0.254\%
\]
4. **Round to the nearest tenth of a percent:**
\[
\text{Relative Error} \approx 0.3\%
\]
### Conclusion
The relative error, rounded to the nearest tenth of a percent, is approximately **0.3%**.
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