1. Significant Digits
Calculations

2. Significant Digits in Calculations
Now you know how to determine the number of significant digits in a number
How do you decide what to do when adding, subtracting, multiplying, or dividing?

3. Rules for Addition and Subtraction
When you add or subtract measurements, your answer must have the same number of decimal places as the one with the fewest
For example: =

4. Addition & Subtraction Continued
Because you are adding, you need to look at the number of decimal places =
(1) (3) (0)
Since you are adding, your answer must have the same number of decimal places as the one with the fewest
The fewest number of decimal places is 0
Therefore, you answer must be rounded to have 0 decimal places
Your answer becomes
105

5. Addition & Subtraction Problems=
23.67 – 500 = = =
95.00 – = 
 -476
 72.14 
20  20.00

6. Rules for Multiplication & Division
When you multiply and divide numbers you look at the TOTAL number of significant digits NOT just decimal places
For example:
x 2.54 =

7. Multiplication & Division
Because you are multiplying, you need to look at the total number of significant digits not just decimal places
x =
(4) (3)
Since you are multiplying, your answer must have the same number of significant digits as the one with the fewest
The fewest number of significant digits is 3
Therefore, you answer must be rounded to have 3 significant digits
Your answer becomes
171

8. Multiplication & Division Problems
x 12.3 =
/ =
(48.12)(2.95) =
58.30 / =
/ =
 1.09 x 104 
 142  

9. More Significant Digit Problems
18.36 g / cm3
°C –23.20 °C
324.5 mi / 5.5 hr
21.8 °C °C
460 m / 5 sec
= g/cm3
= °C
= 59 mi / hr
= °C
= 90 or 9 x 101 m/sec