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.
75.6 times 12.33 = 932.148 correct to 6 significant figures
The least number of significant figures in any number of the problem determines the number of significant figures in the answer which, in this case, would be 932.
16.3*3.9 = 63.57 However, 16.3 and 3.9 are accurate to 1 decimal place, so, the minimum and maximum values of their product are: minimum 16.25*3.85 = 62.56 maximum 16.35*3.95 = 64.58 The only thing one can be sure about is that the answer, to the nearest integer, is between 63 and 65. So, the answer to the correct number of sig figs is 60.
28.26 times pi which is 3.14 equals 88.78 or 88.8 if you need the correct amount of significant figures.
the answer will be 961.6 and it will have 4 significant figures mah friend :)
75.6 times 12.33 = 932.148 correct to 6 significant figures
The least number of significant figures in any number of the problem determines the number of significant figures in the answer which, in this case, would be 932.
It's 10, correct to two significant figures.
There are two significant figures which are the two 2s.
16.3*3.9 = 63.57 However, 16.3 and 3.9 are accurate to 1 decimal place, so, the minimum and maximum values of their product are: minimum 16.25*3.85 = 62.56 maximum 16.35*3.95 = 64.58 The only thing one can be sure about is that the answer, to the nearest integer, is between 63 and 65. So, the answer to the correct number of sig figs is 60.
28.26 times pi which is 3.14 equals 88.78 or 88.8 if you need the correct amount of significant figures.
There are 4 sf. The trailing 0s in 4.00700 must be there for a reason and that reason is that they are significant. But, if you multiply a number with 6 sf by a number with 4 sf then the answer can have at most 4 sf.
the answer will be 961.6 and it will have 4 significant figures mah friend :)
0.2400
12.6 * 0.53 = 6.68 in significiant figures
223.4*7.5=1675.5=1700(sf) There are two significant figures
The product is 67.30879 which means it has 7 significant figures