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Chapter 1: Problem 112

The area of a rectangle of size \(1.25 \times 2.245 \mathrm{~cm}\) in significant figure is ......... (a) \(2.80625 \mathrm{~cm}^{2}\) (b) \(2.81 \mathrm{~cm}^{2}\) (c) \(2.806 \mathrm{~cm}^{2}\) (d) \(2.8062 \mathrm{~cm}^{2}\)

Short Answer

Expert verified
The area of the rectangle rounded to the correct significant figure is \(2.81 \mathrm{~cm}^{2}\), so the correct answer is (b).

Step by step solution

01

Identify the dimensions of the rectangle

We are given the dimensions of the rectangle as \(1.25 \times 2.245 \mathrm{~cm}\). So, the length is \(1.25 \mathrm{~cm}\) and the width is \(2.245 \mathrm{~cm}\).
02

Calculate the area of the rectangle

The formula for calculating the area of the rectangle is: \(Area = length \times width\) Now, we will substitute the values of the dimensions: \(Area = 1.25 \mathrm{~cm} \times 2.245 \mathrm{~cm}\) \(Area = 2.80625 \mathrm{~cm}^{2}\)
03

Round the area to the correct significant figure

The least number of decimal places in the given dimensions is two, so we'll round the area to two decimal places: \(Area \approx 2.81 \mathrm{~cm}^{2}\) Therefore, the area of the rectangle rounded to the correct significant figure is \(2.81 \mathrm{~cm}^{2}\), so the correct answer is (b).

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