Teresa estimates that the height of a giraffe in a zoo is 18 feet in fact it is 16 feet tall what is Teressa percent error use proportional relationships to solve the problem be sure to show all of the work provide your answer as a percant and round your answer to the nearest tenth

To calculate Teresa's percent error in her estimate of the giraffe's height, we can use the formula for percent error:

\[ \text{Percent Error} = \left( \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100 \]

1. Identify the values:

   • Estimated Value = 18 feet
   • Actual Value = 16 feet

2. Calculate the difference: \[ \text{Difference} = \text{Estimated Value} - \text{Actual Value} = 18 - 16 = 2 \text{ feet} \]

3. Plug the values into the percent error formula: \[ \text{Percent Error} = \left( \frac{2}{16} \right) \times 100 \]

4. Calculate the fraction: \[ \frac{2}{16} = 0.125 \]

5. Multiply by 100 to convert to a percentage: \[ \text{Percent Error} = 0.125 \times 100 = 12.5 \]

Therefore, Teresa's percent error in estimating the height of the giraffe is \( \boxed{12.5} \) percent when rounded to the nearest tenth.

Certainly! Let's break down the process of calculating Teresa's percent error step by step.

1. Understanding Percent Error

Percent error is a way to express how much an estimated or measured value deviates from the actual value, relative to the actual value itself. It tells us how inaccurate an estimate is in terms of percentage.

2. Formula for Percent Error

The formula to calculate percent error is:

\[ \text{Percent Error} = \left( \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100 \]

This formula consists of three main parts:

• Estimated Value: This is the value that Teresa guessed or estimated.
• Actual Value: This is the real or measured value.
• Difference: This is the absolute difference between the estimated value and the actual value.

3. Identify the Values

In this problem:

• Teresa estimated the giraffe's height to be 18 feet.
• The actual height of the giraffe is 16 feet.

4. Calculate the Difference

First, we find the difference between the estimated value and the actual value:

\[ \text{Difference} = \text{Estimated Value} - \text{Actual Value} = 18 - 16 = 2 \text{ feet} \]

This means Teresa's estimate was 2 feet higher than the actual height.

5. Plug the Values into the Formula

Now we substitute the values into the formula:

\[ \text{Percent Error} = \left( \frac{2}{16} \right) \times 100 \]

Here, \(2\) is the difference we calculated, and \(16\) is the actual value.

6. Calculate the Fraction

Next, we compute the fraction:

\[ \frac{2}{16} = 0.125 \]

This tells us that 2 feet is 0.125 times the actual height of the giraffe.

7. Convert to Percentage

To express this as a percentage, we multiply by 100:

\[ \text{Percent Error} = 0.125 \times 100 = 12.5 \]

Conclusion

So, the percent error in Teresa's estimate of the giraffe's height is 12.5%. This means that her estimate was off by 12.5% from the actual height of the giraffe.

When rounding to the nearest tenth, we still get 12.5% as the final answer.

Thus, the final answer is \( \boxed{12.5} \) percent.