1. Using Significant Digits
Science 1206-Physics
Using Significant Digits

2. Rules for Determining the Number of Significant Digits :
Any non-zero number
Ex , 51.7 and 5.17 all have 3 sig figs
Any zero between non-zero numbers
Ex , 5057 and all have 4 sig figs
Any trailing zeros after a decimal
Ex , and all have 5 sig figs
Any trailing zeros before a decimal if the value is a known measurement
Ex has 1 sig fig while 100. has 3

3. EXAMPLES Example: Number of Significant Figures: 0.0070 2 50 1 6200. 4
60093 5
5.30 3
5500

4. Using Significant Digits
Addition/Subtraction
When adding and subtracting, the answer must have the same number of decimal places as the measured value with the fewest decimal places
Ex:
1.2 mm mm mm
2.01
- 3.4
Find the sum (or difference), then round to the correct number of sig figs.

5. Continued… Multiplication/Division
Don’t forget the rules for rounding!
Multiplication/Division
When multiplying or dividing, the answer must have the same number of sig figs as the factor with the fewest sig figs
Ex: Area of a triangle
3.2 cm
10.1 cm

6. Examples
= h h =
465 km = x
5.21 h

7. Sometimes have both:
÷ (3.245)(2.05 – 13.6)

8. Scientific Notation: Numbers greater than 10 Numbers less than 1
Have a positive exponent
the exponent is equal to the number of places that the decimal point has been moved to the left.
Ex:
Numbers less than 1
Have a negative exponent
The exponent is equal to the number of places that the decimal point is
moved to the right.
Ex:

9. Many calculators enter it differently

10. Homework Pg 349 # 2, 3 (List # of sig figs), 4, 6
Will be checked and corrected tomorrow!!

11. Homework Check
Pg 349
# 2, 3 (List # of sig figs), 4, 6

12. Continued…
At times, we need to convert from small units to large units, and vice versa
Convert km into m
Convert 45 min into hours
Convert s into hours
Sometimes we can do them in our heads, but it is easy to make mistakes

13. Continued… Conversion Factors:
To convert units, multiply the current number by a conversion factor (equality)
Example: Change 19.5 min into hours.
Step 1: Find the equality  60 min : 1 h
Step 2: Convert the equality into a fraction 
Step 3: Multiply it to convert the units
19.5 min x =
Conversion Factor

14. Practice (Find the conversion factor first)
5.00 km to m 265 m to mm 4.7h to min 23.6h to s