When multiplying and dividing measured quantities, the number of significant figures in the result should be equal to the number of significant figures in _____.
all of the measurements
the least precise measurement
the most precise measurement
the least and most precise measurements
I think b is the best answer of the choices given.
Here is an example: 2.345 x 2.0 = 4.690. There are four significant figures in 2.345 and two in 2.0 so you will be allowed two in the answer. That will be 4.7. Same process in division. I don't look for what I see as the least precise measurement; rather I count the number of s.f. in each of the numbers and use an answer with the least number of s.f. in any of the numbers multiplied. Again, 1 x 2.556 x 3.54 x 9.999999 = 90.48239 but the number 1 has only 1 s.f. so you give the answer as 9E1.
the least precise measurement
When multiplying and dividing measured quantities, the number of significant figures in the result should be equal to the number of significant figures in the least precise measurement.
When multiplying and dividing measured quantities, the number of significant figures in the result should be equal to the number of significant figures in the least precise measurement.
To understand why, we need to consider the concept of significant figures. Significant figures represent the level of precision or certainty in a measured quantity. The rules for determining the number of significant figures in a measurement can be quite complex, but for the purpose of this explanation, we'll focus on the basics.
When performing multiplication or division, the result should be expressed with the same level of precision as the least precise measurement. This is because the least precise measurement determines the accuracy of the calculation. If we were to report the result with more significant figures than the least precise measurement, it would imply a level of precision that isn't supported by the data.
For example, let's say we have two measurements:
Measurement 1: 3.52 cm (3 significant figures)
Measurement 2: 2.4 cm (2 significant figures)
If we were to multiply these two measurements, the calculated result would be 8.448 cm^2. However, we cannot report the result with more significant figures than the least precise measurement, which in this case is Measurement 2 (2 significant figures). Thus, the final answer should be rounded to 8.4 cm^2.
In summary, when multiplying or dividing measured quantities, the number of significant figures in the result should be equal to the number of significant figures in the least precise measurement.