I just do not understand ANYTHING about multiplying/dividing/adding/subtracting significant figures!
For example, the problem is: Solve the following to the correct number of significant figures: (5.039)(0.0074)
What am I supposed to do? Just multiply the numbers? What does that have to do with significant figures? I'm soo confused. Help please?
You need to know the rules for significant figures when multiplying/dividiing (one set of rules) and adding/subtracting (another set of rules).
When multiplying/dividing, the "answer" may have no more significant figures than the least number in the figures used; for example, 5.039 x 0.0074 = 0.0372886 on my calculator. Now look at the numbers used to obtain that value. There are four significant figures in 5.039 and two s.f. in 0.0074. Therefore, the answer may have no more than two s.f. and the value should be rounded to 0.037.
To solve the problem, you need to follow these steps:
1. Multiply the two numbers: 5.039 x 0.0074 = 0.0372886.
2. Now, look at the significant figures in the numbers you used.
- The first number, 5.039, has four significant figures.
- The second number, 0.0074, has two significant figures.
3. According to the rules for multiplying/dividing significant figures, the answer should have no more significant figures than the least number used. In this case, the second number has the least number of significant figures (two).
4. Therefore, you need to round your answer to two significant figures.
- The digit after the second significant figure is 8, which is greater than 5. So you round up the second significant figure (3) to 4.
5. The final answer, to the correct number of significant figures, is 0.037.
I hope this explanation helps clarify the concept of significant figures in multiplication/division.