when using significant figures, why is 2.8023 - 4.762 = -1.960 instead of -1.961
we have 4 significant figures in this problem because
4.762 (four numbers) is not 4.7620 (five )
so the problem is really
2.802 - 4.762 = -1.960
so does this apply to everything else where you round all the numbers down to the number with the least significant figures?
yes, if you only know one of them to 3 decimal places, there is no point in carrying more in the others.
When using significant figures, we follow a set of rules to determine the number of digits in the answer that are significant. In this case, let's consider the numbers and their significant figures:
2.8023 has five significant figures because all non-zero digits are always significant.
4.762 has four significant figures. Similarly, all non-zero digits are significant.
When subtracting, you want to preserve the least number of decimal places from the original numbers. The second number, 4.762, has the least number of decimal places (three) compared to the first number, 2.8023 (four). Therefore, when subtracting, we'll round our answer to three decimal places.
Subtracting the two numbers, 2.8023 - 4.762, we get -1.9597. Now, since we need to round to three decimal places, the third decimal place is a '9', and according to the rounding rules, if the digit in the next decimal place (in this case, '7') is 5 or greater, we round up the last digit.
Thus, the final answer with three significant figures is -1.960.