The actual dimensions of a rectangle are 3cm by 3cm. Carter measures the sides to be 2.75cm by 2.78cm. In calculating the area, what is the relative error, to the nearest hundredth. Answer:

Calculate Actual Area: To find the relative error, we first need to calculate the actual area and the measured area of the rectangle. The actual area is the product of the actual length and width. Actual area = Actual length × Actual width Actual area = 3cm × 3cm Actual area = 9cm²Calculate Measured Area: Next, we calculate the measured area using the measured dimensions. Measured area = Measured length × Measured width Measured area = 2.75cm × 2.78cm Measured area = 7.645cm²Find Absolute Error: Now, we find the absolute error, which is the difference between the actual area and the measured area. Absolute error = |Actual area - Measured area| Absolute error = |9cm² - 7.645cm²| Absolute error = 1.355cm²Calculate Relative Error: The relative error is the absolute error divided by the actual area, usually expressed as a percentage. Relative error = (Absolute error / Actual area) × 100% Relative error = (1.355cm² / 9cm²) × 100% Relative error = 0.1506 × 100% Relative error = 15.06%Round Relative Error: Finally, we round the relative error to the nearest hundredth. Rounded relative error = 15.06% (rounded to two decimal places)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The actual dimensions of a rectangle are
3cm by
3cm. Carter measures the sides to be
2.75cm by
2.78cm. In calculating the area, what is the relative error, to the nearest hundredth.
Answer:

The actual dimensions of a rectangle are $3 \mathrm{~cm}$ by $3 \mathrm{~cm}$ . Carter measures the sides to be $2.75 \mathrm{~cm}$ by $2.78 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest hundredth. $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 7

Percent error: word problems

Full solution

Q. The actual dimensions of a rectangle are

3 \mathrm{~cm}

3 \mathrm{~cm}

. Carter measures the sides to be

2.75 \mathrm{~cm}

2.78 \mathrm{~cm}

. In calculating the area, what is the relative error, to the nearest hundredth.

\newline

Answer:

Calculate Actual Area: To find the relative error, we first need to calculate the actual area and the measured area of the rectangle. $\newline$ The actual area is the product of the actual length and width. $\newline$ Actual area = Actual length $\times$ Actual width $\newline$ Actual area = $3\,\text{cm}$ $\times$ $3\,\text{cm}$ $\newline$ Actual area = $9\,\text{cm}^2$
Calculate Measured Area: Next, we calculate the measured area using the measured dimensions. $\newline$ Measured area = Measured length $\times$ Measured width $\newline$ Measured area = $2.75\,\text{cm} \times 2.78\,\text{cm}$ $\newline$ Measured area = $7.645\,\text{cm}^2$
Find Absolute Error: Now, we find the absolute error, which is the difference between the actual area and the measured area. $\newline$ Absolute error = $|\text{Actual area} - \text{Measured area}|$ $\newline$ Absolute error = $|9\text{cm}^2 - 7.645\text{cm}^2|$ $\newline$ Absolute error = $1.355\text{cm}^2$
Calculate Relative Error: The relative error is the absolute error divided by the actual area, usually expressed as a percentage. $\newline$ Relative error = $(\text{Absolute error} / \text{Actual area}) \times 100\%$ $\newline$ Relative error = $(1.355\,\text{cm}^2 / 9\,\text{cm}^2) \times 100\%$ $\newline$ Relative error = $0.1506 \times 100\%$ $\newline$ Relative error = $15.06\%$
Round Relative Error: Finally, we round the relative error to the nearest hundredth. $\newline$ Rounded relative error = $15.06\%$ (rounded to two decimal places)