1. Calculating with Significant Figures
When we do math with these numbers, always round to the number of significant figures represented by the most uncertain number. There are rules, depending on the operations you perform.

2. Calculating with Significant Figures: Multiplication & Division
To determine the number of significant figures in your answer, look for the term with the smallest number of significant figures, because that is the least accurate measurement:

3. Multiplication Example:
4.56 has three significant figures and 1.4 has two significant figures, therefore round off to two significant figures in your answer = 6.4

4. Division Example:
Example: = Since 298 has the least number of significant figures (3), we round the answer to

5. Multiplication & Division Practice
67.90 ÷ 2
5600 ÷0.368
884.00÷76. ÷
14 x
2,096 x 1.3
47,249 x
38,000 x
536 x

6. Calculating with Significant Figures: Addition & Subtraction
To determine the number of significant figures in your answer, find the term with the smallest number of decimal places. Use that many decimal places for your significant figures in your answer.

7. Addition Example:
Example: Since 18.0 has just one decimal place, we will round off the answer to one decimal place = 31.1

8. Addition & Subtraction Practice
– ,
400. – 1.43 ,

9. Rounding Off
Once you have determined how many significant figures is in your answer, there are a few rules for rounding off:
Round down if the digit to be removed is less than rounded to two significant figures becomes 1.3
Round up if the digit to be removed is 5 or greater Rounding to two significant figures, 1.36 becomes 1.4 and becomes 3.2.
If you are removing a string of numbers, only look at the first number to the right Rounding to two significant figures becomes 4.3.
In a series of calculations, keep the extra digits until your final result, then round.

10. Scientific Notation The mass of a proton = 1.67 x 10-27 grams
What does this mean???

11. Review: What are the following #s?
101
102
103
104
100
=10
=10x10=100
=10x10x10=1,000
= 10,000
= 1
10-1
10-2
10-3
10-4
= .1
= .01
= .001
= .0001

12. Scientific Notation uses a number multiplied by a power of ten:
2000 = 2x103
0.004 = 4x10-3

13. Rules for Scientific Notation:
Add decimal point if it is missing:
Move decimal point so there is ONE non-zero number to the left of it:
Exponent is the number of places the decimal point was shifted: x103
Exponent can be positive or negative: = 6.3x10-3

14. Express in Scientific Notation
4001
32,560,000
78,941,000,000