Which of the answers for the following conversions contains the correct number of significant figures?
A)2.543 m x 39.4in/1m=100.1924in
B)2 L x 1.06qt/1L=2.12 qt
C)24.95 min x 1hr/60 min=0.4158 hr
D)12.0 ft x 12in/1ft x 2.54cm/1in=370cm
E)24.0 kg x 1lb/2.20kg=11lb
the answer is c but i don't understand why. i thought you round the answer based on the number of sig figs of the lowest measurement so why wouldn't D be the answer?
C is correct
D is correct if the zero has a line over it (ie, a significant zero)
c is correct becaues 1hr/60 min is NOT a measurement, it is a fundamental conversion. 1hr/60min is an infinite number of significant digits.
d is correct only if the last zero is designated as significant, we once put a line over the zero to indicated it is significant. It doesn't show that here.
but i though d would be rounded to 2 sf, not 3 because of the 12 in. or is that wrong because 12in/ft is not a measured number?
Ah, the world of significant figures! It can be quite confusing, but let's try to make some sense out of it, shall we?
In this case, we need to consider the rules for multiplication and division with significant figures. The general rule is that the answer should have the same number of significant figures as the measurement with the fewest significant figures.
Now, let's look at the options:
A) 100.1924in: This has 7 significant figures, but we take the fewest significant figures from the initial measurement, which is 2.543m with 4 significant figures. So, A is not the correct answer.
B) 2.12 qt: This has 3 significant figures, but the initial measurement, 2L, has only 1 significant figure. So, B is not the correct answer either.
C) 0.4158 hr: This has 4 significant figures, and the initial measurement, 24.95 min, also has 4 significant figures. Therefore, C is the correct answer!
D) 370 cm: You're absolutely right in thinking that you should round the answer based on the lowest number of significant figures in the initial measurements. However, in this case, the initial measurements are both exact numbers (12.0 ft and 2.54 cm) and therefore have infinite significant figures. So, D is not the correct answer.
E) 11 lb: Similar to D, the initial measurements in this case, 24.0 kg and 2.20 kg, are also exact numbers. Thus, they have infinite significant figures. So, E is not the correct answer either.
I hope that clears things up! Just remember, sometimes the rules of significant figures can be a little tricky, but with a little practice, you'll get the hang of it!
To determine the correct number of significant figures in a conversion, you need to consider the significant figures in the given measurements and the conversion factors.
Let's analyze each conversion:
A) 2.543 m x 39.4 in/1 m = 100.1924 in
In this conversion, 2.543 m has 4 significant figures, and 39.4 in/1 m is an exact equivalent (no uncertainty regarding its value). Therefore, the correct answer should have 4 significant figures. But the result, 100.1924 in, has 7 significant figures, which is more than the original measurement. Thus, option A is not correct.
B) 2 L x 1.06 qt/1 L = 2.12 qt
In this conversion, both 2 L and 1.06 qt/1 L have infinite significant figures because they are defined values. When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures. Here, both measurements have an indefinite number of significant figures, so the result can also have an indefinite number of significant figures. Thus, option B is not correct.
C) 24.95 min x 1 hr/60 min = 0.4158 hr
In this conversion, 24.95 min has 4 significant figures, and 1 hr/60 min is an exact equivalent. Therefore, the result, 0.4158 hr, also has 4 significant figures, matching the original measurement. Thus, option C is correct.
D) 12.0 ft x 12 in/1 ft x 2.54 cm/1 in = 370 cm
In this conversion, 12.0 ft has 3 significant figures, and the conversion factors are exact equivalents. Therefore, the result, 370 cm, also has 3 significant figures, matching the original measurement. Thus, option D could also be correct.
E) 24.0 kg x 1 lb/2.20 kg = 11 lb
In this conversion, 24.0 kg has 3 significant figures, and 1 lb/2.20 kg is an exact equivalent. Therefore, the result, 11 lb, also has 2 significant figures, which is less than the original measurement. Thus, option E is not correct.
Regarding your confusion with option D, it should be noted that while rounding the result based on the measurement with the fewest significant figures is a general rule, it does not apply when there are exact equivalents or conversion factors involved. In D, the conversion factors are exact (1 ft/12 in and 2.54 cm/1 in), so the result does not need to be rounded based on significant figures.
In conclusion, the correct answer is C (24.95 min x 1 hr/60 min = 0.4158 hr) because the result has the same number of significant figures as the original measurement.