Chemistry Reference
In-Depth Information
ADDITION AND SUBTRACTION
In the answers to addition and subtraction problems, the estimated digit that is
farthest to the left is the last digit that can be retained. For example, let's add
6.2 cm and 9.203 cm:
Estimated digits
6.2
cm
9.203 cm
15.403 cm £ 15.4 cm
The leftmost estimated digit is the last digit that can be retained in the answer.
The digit 2 in 6.2 cm is an estimated digit; it has some uncertainty in it. There-
fore, the digit 4 in the answer is also uncertain, and 0 and 3 are completely
unknown. We cannot report the value 15.403 cm, or the reader will believe
that 3 is the only uncertain digit. We must reduce the number of digits to leave
4 as the last digit. In general, we increase the last digit retained if the first
digit to be dropped is 5 or greater; otherwise we leave that last digit
unchanged.
Thus, for addition or subtraction, we retain digits in an answer only as far
to the right as the leftmost uncertain digit in any of the numbers being added
or subtracted. Note that the
number
of significant digits does not matter for addi-
tion or subtraction; what matters is
where the last digits lie.
In the previous
calculation, there are two significant digits in the first number and four in the
second, but the answer has three.
EXAMPLE 2.41
Calculate the sum of 10.10 cm
1.332 cm
6.4 cm.
Solution
10.10 cm
1.332 cm
6.4
cm
17.832 cm £ 17.8 cm
Practice Problem 2.41
Calculate the answer to the proper precision:
62.44 cm
7.145 cm
27.7 cm
MULTIPLICATION AND DIVISION
For multiplication and division, the number of significant digits in the factor
with the fewest significant digits limits the number of significant digits in the
answer. For example, let's multiply 4.1 cm by 21.07 cm:
86.387 cm
2
4.1 cm
21.07 cm
(Incorrect number of significant digits)
