1. Significant Figures
Every measurement has a limit on its accuracy based on the properties of the instrument used.
we must indicate the precision of the measurement by using the correct number of significant figures
Precision – the consistency of a measurement, how repeatable it is

2. Can you name this significant figure?

3. Check your answer with the person next to you
Object A, measured with Ruler I should be recorded as ________
  but as measured with Ruler II should be recorded as _________
Check your answer with the person next to you

4. Check your answer with the person next to you
Object B, measured with Ruler I is  _______________
Object B, measured with Ruler II is _______________
Check your answer with the person next to you

5. Which ruler is the most precise?
Which ruler is the least accurate?

6. What happens if an object is directly on the 3 of the ruler
What happens if an object is directly on the 3 of the ruler? What decimal place to record?

7. Check your answer with the person next to you
what is its smallest division?  _________
How should measurements using Ruler IV be recorded (to how many decimal places)? ________
Check your answer with the person next to you

8. Rules for SigFigs Nonzero digits are ALWAYS significant
Zeroes are only sometimes significant…
All final zeroes after a decimal point are significant
Zeroes between two other significant digits are always significant
Zeroes used soley as placeholders are NOT significant
Zeroes between a decimal point and a nonzero digit are NOT significant.

9. Some examples
m            s        m  
$18,000                $18,000.00             $18,000.    
  cm              

10. 1. Give the number of sig. fig
1. Give the number of sig. fig. and the number of decimal places in each of the number below.
  a)    b)    c)    d)    e)  3,000   f)  3,000.   g)  3,000.00

11. # of sig. fig.
# of decimal places
a) 72.32 4 2 b) 5 3
c)  0.003 1 d)
e) 3,000
assume 1
f) 3,000.
g) 3,000.00 6

12. 2. These numbers have ambiguous zeroes
2. These numbers have ambiguous zeroes. Remove the ambiguity by expressing them in scientific notation.
  a)  in 2 sig. fig.   b)  in 3 sig. fig.   c)  in 4 sig. fig.   d)  2100 in 3 sig. fig.   e)  790,000 in 4 sig. fig.   f)  3800 x 10-7 in 3 sig. fig.

13. Answers
a) in 2 sig. fig.
4.2 x104
b) in 3 sig. fig.
4.20 x 104
c) in 4 sig. fig.
4.200 x 104
d) 2100 in 3 sig. fig.
2.10 x 103
e) 790,000 in 4 sig. fig.
7.900 x 105
f) 3800 x 10-7 in 3 sig.fig.
3.80 x 10-4

14. When you perform any arithmetic operation, it is important to remember that the result can never be more precise than the least precise measurement.  

15. Adding and Subtracting
To add or subtract measurements, first perform the operation, then round off the result to correspond to the least precise value involved.  For example, add these values:
m m m   =    m  
3.21m
Least precise measurement? ______
Round answer to _______
30.24m

16. Multiply and Divide
After performing the calculation, note the factor that has the least number of significant digits.  Round the product or quotient to this number of digits.  For example, multiply
3.22 cm by 2.1 cm  =  cm2   
corrected to  _________
6.8 cm2

17. 36.5 m divided by 3.414 s = 10.691 m/s corrected to ________
Divide these two measurements and report answer with correct number of significant digits
36.5 m divided by s  = m/s corrected to ________
10.7 m/s

18. Let’s review… Some Practice problems 1) 2804m 2) 2.84km 3)0.029m
            
4) m  5)   4.6x105m  6)   4.06x105m  
7)   750m         8)  75m          9)75,000 m  
        
10)   75,000. m   11)  75,000.0m  12)  10 cm

19. Answers Some Practice problems 1) 2804m 2) 2.84km 3)0.029m
            
4) m  5)   4.6x105m  6)   4.06x105m  
7)   750m         8)  75m          9)75,000 m  
        
10)   75,000. m   11)  75,000.0m  12)  10 cm

20. More practice! 1) 6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = ?
2)     1.6 km   +   1.62 m   +    1200 cm   =   ?
3)     g   -   7.8 g   =    ?
4)     m   -   6.0 m    =   ?
5)     m   +  kg   =   ?
6)     131 cm  x  2.3 cm   =   ?
7)     m  x  m   =  ?
8)    20.2 cm   divided by  7.41 s   =   ?
9)    g  divided by  ml  =  ?