Express the following quantities to the correct number of significant figures:
(a) 23.043 ± 4.321
(b) 67 ± 9.023
(c) 33.1492934 ± 2
Isn't (a) already the correct number of significant digits?
Would (b) be 67.000 ± 9.023?
Would (c) be 33.1492934 ± 2.0000000
or would
(a) 23.04 ± 4.321
(b) 67 ± 9.0
(c) 30 ± 2
b) you cant add precision to 67
67+-9
c) it is correct as written.
which of the a answers are right?
and which of c?
To express quantities with the correct number of significant figures, you need to consider the rules for rounding.
(a) 23.043 ± 4.321:
The rule is to round to the same number of decimal places as the least precise measurement. In this case, 4.321 has three decimal places, so the result should have three decimal places as well. Therefore, the correct expression is:
23.043 ± 4.321
(b) 67 ± 9.023:
The rule is to round to the same number of decimal places as the least precise measurement. In this case, 9.023 has three decimal places, so the result should have three decimal places as well. Therefore, the correct expression is:
67 ± 9.023
(c) 33.1492934 ± 2:
The rule is to round to the same number of decimal places as the least precise measurement. In this case, 2 has no decimal places, so the result should have no decimal places as well. Therefore, the correct expression is:
33 ± 2
To express quantities to the correct number of significant figures, follow these guidelines:
(a) 23.043 ± 4.321:
The given value has five significant figures, and the uncertainty has four significant figures. To express the quantity to the correct number of significant figures, we need to consider the least number of significant figures in the given value and the uncertainty. In this case, the uncertainty has four significant figures, so we round the given value to four significant figures. Therefore, the quantity can be expressed as 23.04 ± 4.321.
(b) 67 ± 9.023:
The given value has two significant figures, and the uncertainty has four significant figures. Again, we consider the least number of significant figures between the given value and the uncertainty. In this case, the given value has only two significant figures, so we cannot have more significant figures in the uncertainty. Therefore, the quantity can be expressed as 67 ± 9.0.
(c) 33.1492934 ± 2:
The given value has nine significant figures, and the uncertainty has only one significant figure. To express the quantity to the correct number of significant figures, we consider the least number of significant figures between the given value and the uncertainty. In this case, the uncertainty has only one significant figure, so we round the given value to one significant figure. Therefore, the quantity can be expressed as 33 ± 2.
Using this approach, the correct expressions would be:
(a) 23.04 ± 4.321
(b) 67 ± 9.0
(c) 33 ± 2