A dishwasher has a mass of exactly 49.6 kg. Measured the mass of the dishwasher as 50kg to the nearest kg. A- find the absolute error. B- find relative error at 3 decimal places. C- find percentage error at 2 decimal places.

Let's solve this step by step.

**Given:**
- Actual mass of the dishwasher = 49.6 kg
- Measured mass = 50 kg

### A. Absolute Error:
The absolute error is the difference between the measured value and the actual value.

\[
\text{Absolute Error} = |\text{Measured Value} - \text{Actual Value}|
\]

\[
\text{Absolute Error} = |50 - 49.6| = 0.4 \, \text{kg}
\]

### B. Relative Error:
The relative error is the ratio of the absolute error to the actual value.

\[
\text{Relative Error} = \frac{\text{Absolute Error}}{\text{Actual Value}}
\]

\[
\text{Relative Error} = \frac{0.4}{49.6} \approx 0.008
\]

Rounded to 3 decimal places, the relative error is:

\[
\text{Relative Error} = 0.008
\]

### C. Percentage Error:
The percentage error is the relative error expressed as a percentage.

\[
\text{Percentage Error} = \text{Relative Error} \times 100
\]

\[
\text{Percentage Error} = 0.008 \times 100 = 0.806
\]

Rounded to 2 decimal places, the percentage error is:

\[
\text{Percentage Error} = 0.81\%
\]

### Summary:
- A. Absolute Error = **0.4 kg**
- B. Relative Error = **0.008**
- C. Percentage Error = **0.81%**

Let me know if you'd like more details on these calculations, and here are a few related questions you might want to explore:

1. What is the absolute error when the actual mass is 60 kg and the measured mass is 61 kg?
2. How does the relative error change if the actual value is much smaller, say 25 kg?
3. If the measured mass was 49.4 kg instead of 50 kg, what would be the new percentage error?
4. Can absolute error ever be negative, and why?
5. What are typical acceptable percentage errors in scientific experiments?

**Tip:** When calculating relative or percentage errors, always use the actual value in the denominator to get an accurate ratio!

A dishwasher has a mass of exactly 49.6 kg. Measured the mass of the dishwasher as 50 kg to the nearest kg. A- find the absolute error. B- find relative error at 3 decimal places. C- find percentage error at 2 decimal places.

Learn how to find the absolute, relative, and percentage error for a dishwasher mass measurement. This problem involves calculating the absolute error, relative error to 3 decimal places, and percentage error to 2 decimal places. Suitable for Grades 6-8 students.

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