Question

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm respectively. Find the area of the sheet in appropriate significant figures and the ERROR?

Answer 1

Answer:

Area is 163.62 cm²

The absolute error in calculation of the area is 1.31

Explanation:

The formula of finding the area of the rectangular sheet is :

Length × breath

So here our length is 16.2 cm and our breadth is 10.1 cm

So we multiply them

16.2 cm × 10.1 cm = 163.62 cm²

We then proceed to calculating the error in multiplication

To find the error in multiplication we first find the error in the measurement of the length and the breadth.

The units have each been given to one decimal place I.e 0.1

So we find half of the decimal place to which the units have been given

½ × 0.1 = 0.05

We then find the maximum and minimum units because the measurement might have had a higher or lower error.

16.2 + 0.05 = 16.25 cm

10.1 + 0.05 = 10.15 cm

We then find the maximum area

16.25 × 10.15 = 164.94 cm²

We then proceed to the minimum area

16.2 - 0.05 = 16.15 cm

10.1 - 0.05 = 10.05 cm

16.15 × 10.05 = 162.32cm²

To find the absolute error in calculation of the multiplication we use the following formula

½(maximum area - minimum area)

164.94 - 162.32 = 2.62

½ × 2.62 = 1.31

So the absolute error is 1.31

Answer 2

Explanation:

$\large \tt absolute \: \: \: error \: \: = 1.31$