Question
What is the explanation for calculating the greatest possible error in a measurement of 0.20 kilometers?
Answers
GPT-4o mini
The greatest possible error in a measurement is often referred to as the "absolute error" and can be expressed in terms of the precision of the measurement. For a measurement of 0.20 kilometers, we determine the greatest possible error based on the rounding of the measurement.
1. **Identify the Measurement**: The measurement is 0.20 kilometers.
2. **Determine the Precision**: The number 0.20 is expressed to two decimal places, which indicates a precision of 0.01 kilometers.
3. **Calculate the Greatest Possible Error**: The greatest possible error is typically half of the smallest unit of measure represented in the measurement. Since 0.20 kilometers is precise to the hundredths place (0.01 km), the error is half of that:
\[
\text{Greatest Possible Error} = \frac{0.01 \text{ km}}{2} = 0.005 \text{ km}
\]
4. **Interpretation**: This means that the actual value could be as much as 0.005 kilometers above or below the measured value of 0.20 kilometers. Therefore, the true value could range from:
\[
0.20 \text{ km} - 0.005 \text{ km} = 0.195 \text{ km}
\]
to
\[
0.20 \text{ km} + 0.005 \text{ km} = 0.205 \text{ km}
\]
Thus, the greatest possible error in the measurement of 0.20 kilometers is ±0.005 kilometers.
1. **Identify the Measurement**: The measurement is 0.20 kilometers.
2. **Determine the Precision**: The number 0.20 is expressed to two decimal places, which indicates a precision of 0.01 kilometers.
3. **Calculate the Greatest Possible Error**: The greatest possible error is typically half of the smallest unit of measure represented in the measurement. Since 0.20 kilometers is precise to the hundredths place (0.01 km), the error is half of that:
\[
\text{Greatest Possible Error} = \frac{0.01 \text{ km}}{2} = 0.005 \text{ km}
\]
4. **Interpretation**: This means that the actual value could be as much as 0.005 kilometers above or below the measured value of 0.20 kilometers. Therefore, the true value could range from:
\[
0.20 \text{ km} - 0.005 \text{ km} = 0.195 \text{ km}
\]
to
\[
0.20 \text{ km} + 0.005 \text{ km} = 0.205 \text{ km}
\]
Thus, the greatest possible error in the measurement of 0.20 kilometers is ±0.005 kilometers.