determine the correct answers to the calculation shown below to the correct number of significant figures?
a. (32.453)(34.23+1.17)/(2.26-1.811)(0.00378)=9.671716784=9.7
b. (3.23+0.0018)=3.2318=3.2
c. (82.97-0.012)/(1.100)(21.9)=1651.618364
would you tell me please are the answers corect?
a.
Assuming I understand the calculation as presented as I don't get the same numerical answers.
(32.453)(34.23+1.17)/(2.26-1.811)(0.00378)=
(32.453)(35.40)/(0.50)(0.00378)
(retaining the least precise decimal places)
the next step will need to retain the sig figs. The least sig figs is two (0.50)
(32.453)(35.40)/(0.50)(0.00378)
=607849
which is 6.1 x 10^5 to two sig figs
b.
(3.23+0.0018)=3.2318=3.23
the least precise is the two dp in 3.23
c. (82.97-0.012)/(1.100)(21.9) =
(82.96)/(1.100)(21.9)
For the next step the least number of significant figures is three (21.9)
(82.96)/(1.100)(21.9) =
3.44 to three sig figs
To determine the correct number of significant figures in a calculation, you need to follow a few rules:
1. Addition and Subtraction:
- The result should have the same number of decimal places as the quantity with the fewest decimal places.
2. Multiplication and Division:
- The result should have the same number of significant figures as the quantity with the fewest significant figures.
Now, let's apply these rules to each calculation:
a. (32.453)(34.23 + 1.17) / (2.26 - 1.811)(0.00378) = 9.671716784
In the parentheses, there are three numbers: 34.23, 1.17, and 2.26. Among these three, the number with the fewest significant figures is 2.26, which has three significant figures. Therefore, the answer should also have three significant figures. Rounding the answer to three significant figures, we get 9.67. So, the correct answer is 9.67.
b. (3.23 + 0.0018) = 3.2318
Here, we are only performing addition. To determine the number of significant figures in the result, we look at the number with the fewest decimal places, which is 0.0018. It has four significant figures. Therefore, the result should also have four significant figures. Rounding 3.2318 to four significant figures, we get 3.232. However, when considering the original numbers, 3.23 and 0.0018, the digit in the thousandths place is uncertain. So, the correct answer would be 3.2.
c. (82.97 - 0.012) / (1.100)(21.9) = 1651.618364
In this calculation, we have two sets of multiplication: (1.100)(21.9) and (82.97 - 0.012). Among these two, the set with the fewest significant figures is (1.100)(21.9), which has four significant figures. Therefore, the result should have four significant figures. Rounding 1651.618364 to four significant figures, the correct answer is 1652.
To summarize:
a. The correct answer is 9.67.
b. The correct answer is 3.2.
c. The correct answer is 1652.