Heather estimated the volume of her bathtub to be 38 gal. The actual volume of her bathtub was 35 gal. Find the absolute error and the percent error of Heather's estimate. If necessary, round your answers to the nearest tenth. absolute error $$ =\square \mathrm{gal} $$ percent error $$ =\square \% $$

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UpStudy AI · Accepted Answer

To find the absolute error and the percent error of Heather's estimate, we can follow these steps:

1. **Calculate the Absolute Error:**
   The absolute error is the difference between the estimated value and the actual value. It can be calculated using the formula:
   $$
   \text{Absolute Error} = |\text{Estimated Value} - \text{Actual Value}|
   $$

2. **Calculate the Percent Error:**
   The percent error is calculated using the formula:
   $$
   \text{Percent Error} = \left( \frac{\text{Absolute Error}}{\text{Actual Value}} \right) \times 100\%
   $$

Now, let's plug in the values:

- Estimated Value = 38 gal
- Actual Value = 35 gal

### Step 1: Calculate the Absolute Error
$$
\text{Absolute Error} = |38 - 35| = |3| = 3 \text{ gal}
$$

### Step 2: Calculate the Percent Error
$$
\text{Percent Error} = \left( \frac{3}{35} \right) \times 100\%
$$

Now, let's calculate the percent error.

$$
\text{Percent Error} = \left( \frac{3}{35} \right) \times 100 \approx 8.5714\%
$$

Rounding to the nearest tenth:
$$
\text{Percent Error} \approx 8.6\%
$$

### Final Answers:
- Absolute error $$ = 3 \text{ gal} $$
- Percent error $$ = 8.6\% $$
Absolute error $$ = 3 \text{ gal} $$ Percent error $$ = 8.6\% $$

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