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.
To find the product of 3.15 m and 2 m, you multiply the two values: (3.15 \times 2 = 6.30) m². However, the number of significant figures must be considered. The value 3.15 has three significant figures, while 2 has one significant figure. Therefore, the result should be reported with one significant figure, which gives a final answer of 6 m².
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.
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.
There are two significant figures which are the two 2s.
28.26 times pi which is 3.14 equals 88.78 or 88.8 if you need the correct amount of significant figures.
When multiplying numbers, the result should have the same number of significant figures as the original number with the fewest significant figures. In this case, 400 has one significant figure, and 185 has three significant figures. Therefore, the result of multiplying 400 by 185 will have one significant figure. The answer would be 70,000.
To find the product of 3.15 m and 2 m, you multiply the two values: (3.15 \times 2 = 6.30) m². However, the number of significant figures must be considered. The value 3.15 has three significant figures, while 2 has one significant figure. Therefore, the result should be reported with one significant figure, which gives a final answer of 6 m².
Avogadro's number is typically expressed as (6.022 \times 10^{23}) and has four significant figures. The digits 6, 0, 2, and 2 are significant, while the exponent does not contribute to the count of significant figures. Thus, when using Avogadro's number in calculations, it's important to maintain these four significant figures for accuracy.
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.
To express the measurement 37.26 m × 2.7 m × 0.0015 m in correct units and significant figures, first calculate the product: (37.26 \times 2.7 \times 0.0015 = 0.150165 m^3). The significant figures in the calculation are determined by the least precise measurement, which is 2.7 m (with 2 significant figures). Therefore, the final result should be rounded to 0.15 m³.
0.2400