Problem 5 on Units & Dimensions

Description:

Problem

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the Area and Volume of the sheet to correct significant figures.

Solution

Given in the problem,

Length = 4.234 m, Contains 4 significant digits

Breadth = 1.005 m, Contains 4 significant digits

Height = 2.01 cm = 2.01 × 10⁻² m, Contains 3 significant digits

Calculating Area,

Area = 4.234 × 1.005 m² = 4.25517 m²

Above result is obtained by pure multiplication. But the result of multiplication should contain only as many significant digits as there is in the original number the with least number of significant digits.

Now, the original numbers, 4.234 and 1.005, both contain 4 significant digits. Hence, the result should also contain 4 significant digits.

Hence,

Area = 4.255 m²

Calculating Volume,

Volume = 4.234 × 1.005 × 2.01 × 10^-2 m³

Thickness value is converted to ‘meters’ and then put in the expression.

= 8.5528917 × 10^-2 m³

Again, above result is obtained by pure multiplication. But the result of multiplication should contain only as many significant digits as there is in the original number the with least number of significant digits.

Among the original numbers, 4.234, 1.005 and 2.01, the last one contains the least number of significant digits (Three). Therefore, we round off the result up to 3 significant digits.

Volume = 8.55 × 10^-2 m³