Adding/subtracting sig figs

Question

The question is to solve and express result with correct sig figs.

1.00876 + 0.87206-0.0996. 

 

The first thing I did was the addition first and got 1.88082 then with the sig figs it becomes 1.8808 . Then I subtracted this with 0.0996 and the final answer I got is 1.78. The book says the real answer is 1.7812 but I dont understand because arent you supposed to simplify the answer to the least amount of sig figs?

Answer 1

The number with the least number of decimal places will rule them all... when adding or subtracting.  It's a little different rule than for multiplying and dividing when decimals are involved and that can be confusing. 

 

1.00876 has five decimal places.

0.87206 also has five.

0.0996 only has four.  If it were written 0.09960 then it would have five -- in science when values are written they taken on an extra meaning about how accurate the value could be.

 

So the answer must be rounded to the fourth decimal place which it was, but only AFTER doing the adding and subtracting the way we all learned in math class.  1.78122 would be what we'd write for math class, but only the fourth decimal place is significant, so rounding rules tell you to drop the second 2.  Does that make more sense now?