What is cm times cm in correct number of significant figures?

Answer 1

If the two measures are x cm and y cm, both to the nearest cm, then the lower and upper bounds for the two measures are (x - 0.5 and x + 0.5) and (y - 0.5 , y + 0.5).

Calculate a1 = (x - 0.5)*(y - 0.5) the lower bound for their product and a2 = (x + 0.5)*(y + 0.5) the upper bound for their product. The correct number of significant figures for the answer, a, is the number of digits to which the rounded versions of a1 and a2 agree.

If a and b are small, then you may not get any sig figs this way and you will have to settle for 1 sf, and give the (a1, a2) range in the answer.

Example:

200 cm * 300 cm.

a1 = 199.5*299.5 = 59750.25 cm^2

a2 = 200.5*300.5 = 60250.25 cm^2

These agree to 60000 cm^2 - two sig figs.

20 cm * 30 cm.

a1 = 19.5*29.5 = 575.25 cm^2

a2 = 20.5*30.5 = 625.25 cm^2

These agree to 600cm^2 - one sig fig.

2 cm * 3 cm.

a1 = 1.5*2.5 = 3.75 cm^2

a2 = 2.5*3.5 = 8.75 cm^2

These do not agree to any number if sig figs so simply use 2*3 = 6 cm^2, quoting 3.75 to 8.75 cm^2 as the possible range.