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

Can you name this significant figure?

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

Object B, measured with Ruler I is  _______________Object B, measured with Ruler II is _______________

Check your answer with the person next to you

Which ruler is the most precise?

Which ruler is the least accurate?

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

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

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.

Some examples

0.0860 m            1.0030 s        0.000010203 m  $18,000                $18,000.00             $18,000.    

 0.10001 cm              

• 1. Give the number of sig. fig. and the number of decimal places in each of the number below.

•   a)  72.32   b)  10.002   c)  0.003   d)  0.00170   e)  3,000   f)  3,000.   g)  3,000.00

  # of sig. fig. # of decimal places

a) 72.32 4 2

b) 10.002 5 3

c)  0.003 1 3

d) 0.00170 3 5

e) 3,000 assume 1 0

f) 3,000. 4 0

g) 3,000.00 6 2

• 2. These numbers have ambiguous zeroes. Remove the ambiguity by expressing them in scientific notation.

•   a)  42000 in 2 sig. fig.   b)  42000 in 3 sig. fig.   c)  42000 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.

Answers

a) 42000 in 2 sig. fig. 4.2 x104

b) 42000 in 3 sig. fig. 4.20 x 104

c) 42000 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

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

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:

• 24.686 m + 2.343 m + 3.21 m   =    30.239 m  

Least precise measurement? ______

Round answer to _______

3.21m

30.24m

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  =  6.762 cm2   

• corrected to  _________6.8 cm2

• Divide these two measurements and report answer with correct number of significant digits

• 36.5 m divided by 3.414 s  = 10.691 m/s corrected to ________10.7 m/s

Let’s review…

• Some Practice problems

1) 2804m            2)   2.84km   3)0.029m 

            

4)0.003068m  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

Answers• Some Practice problems

1) 2804m            2)   2.84km   3)0.029m 

            

4)0.003068m  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

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)     8.264 g   -   7.8 g   =    ?4)     10.4168 m   -   6.0 m    =   ?5)     12.00 m   +  15.001 kg   =   ?6)     131 cm  x  2.3 cm   =   ?7)     5.7621 m  x  6.201 m   =  ?8)    20.2 cm   divided by  7.41 s   =   ?9)    40.002 g  divided by  13.000005 ml  =  ?