But what if the number is . in which the insignificant digit is . Here, the convention is that if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by . Then, the number .
rounded off to three significant figures becomes . . On the other hand, the number . rounded off to three significant figures becomes .
since the preceding digit is odd. In any involved or complex multi-step calculation, you should retain, in intermediate steps, one digit more than the significant digits and round off to proper significant figures at the end of the calculation. Similarly, a number known to be within many significant figures, such as in .99792458 × m/s for the speed of light in vacuum, is rounded off to an approximate value × m/s , which is often employed in computations. Finally, remember that exact numbers that appear in formulae like π in T L g = π , have a large (infinite) number of significant figures.
The value of π = .1415926.... is known to a large number of significant figures. You may take the value as . or .
for π , with limited number of significant figures as required in specific cases. Example . Each side of a cube is measured to be . m.
What are the total surface area and the volume of the cube to appropriate significant figures? Answer The number of significant figures in the measured length is . The calculated area and the volume should therefore be rounded off to significant figures. Surface area of the cube = ( .
) m = .299254 m = . m Volume of the cube = ( . ) m = .714754 m = . m Example .
. g of a substance occupies . cm . Express its density by keeping the significant figures in view.
Answer There are significant figures in the measured mass whereas there are only significant figures