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.
Area = 4.255 m² Volume = 0.0855 m³
Explanation
This question tests the application of significant figures in multiplication operations. According to the textbook context, when experimental data are combined through multiplication, the result should be expressed with the same number of significant figures as the measurement with the least significant figures. The thickness (2.01 cm) has only 3 significant figures, which limits the volume calculation to 3 significant figures, while both length and breadth have 4 significant figures each, so the area is expressed to 4 significant figures.
Solution Steps
Step 1: Convert thickness to meters Thickness = 2.01 cm = 2.01/100 m = 0.0201 m
Step 2: Calculate Area Area = Length × Breadth = = 4.25517 m²
Step 3: Apply significant figures rule for Area Length (4.234) has 4 significant figures, Breadth (1.005) has 4 significant figures. Since both have 4 significant figures, Area should have 4 significant figures. Area = 4.255 m² (rounded to 4 significant figures)
Step 4: Calculate Volume Volume = Length × Breadth × Thickness = × 0.0201 = 0.085528917 m³
Step 5: Apply significant figures rule for Volume Length has 4 sig figs, Breadth has 4 sig figs, Thickness (2.01) has 3 sig figs. The result should have the least number of significant figures = 3. Volume = 0.0855 m³ (rounded to 3 significant figures)