Functions with Significant Figures
Adding and Subtracting with the Appropriate Number of Significant Figures
The Rule: When adding and subtracting with sig figs, the answer is expressed according to the least exact factor. The answer is
expressed with the same # of number places as factor farthest to the left.
What this means: Suppose you were adding two numbers:
The Rule: When adding and subtracting with sig figs, the answer is expressed according to the least exact factor. The answer is
expressed with the same # of number places as factor farthest to the left.
What this means: Suppose you were adding two numbers:
When you add these together using your calculator, your calculator comes up with the following answer:
However, your calculator (and you) assume that there are zeros trailing after the 5 in 30.5. If these are measurements, we must conclude that the device that measured 30.5 was not as accurate as the device that measured 1.973. Therefore, because the instrument was less accurate, and the device cannot measure to that decimal place, we cannot assume that those numbers are zeros.
Since we do not know what the numbers are, we cannot add 73 to them. When listing answers to functions, we want to put just the answers we know for sure, so the answer (due to rounding)becomes:
The same would be true for subtraction:
Multiplying and Dividing with the Appropriate Number of Significant Figures
The Rule: When multiplying & dividing, the answer is expressed with same # of sig figs as factor with least # of sig figs.
What this means: Suppose you were multiplying two numbers:
The Rule: When multiplying & dividing, the answer is expressed with same # of sig figs as factor with least # of sig figs.
What this means: Suppose you were multiplying two numbers:
When you multiply these values together using your calculator, your calculator comes up with the following answer:
Again, the answer your calculator gives you does not have the appropriate number of sig figs. When multiplying, you need to determine how many sig figs are in your original values:
Determine which value has the least number of sig figs:
Then, re-write your calculator's answer with the same number of sig figs as the value with the least sig figs:
In the case above, 708.84 needs to be expressed with only 2 significant figures. Therefore, with rounding, you may be tempted to write 71. However, 71 is not near 708.84. We need to write the number with the appropriate number of sig figs, but still be close to the right number. Additional zeros may be needed to be added to do this. As long as you don't add a decimal place though, the number will still have the same number of sig figs. In this case, 71 can become 710, which still has 2 sig figs, and is close in value to 708.84.
The same would be true for dividing:
The same would be true for dividing: