Significant Figures

Scientists use varying pieces of equipment. Different pieces of equipment measure to a different degree of preciseness.
For example : One scale might measure to the hundredths place (.12) while another scale might measure to the thousandths (.120).

We have to account for this when we add, subtract, multiply, or divide numbers of varying preciseness.

We do this by using Significant Figures.

Rules:

1. Any non-zero number (1-9) is significant.
Ex.
      12 has 2 significant figures: 12
           - both 1 and 2 are non-zeroes

      12.3 has 3 significant figures:  12.3
           - 1, 2, and 3 are non-zeroes

2. Any zero between a non-zero is significant.
Ex.
      101 has 3 significant figures: 101
           - 1 is significant (Rule #1)
           - the zero is between the ones     
    
     1002 has 4 significant figures: 1001
          - 1 and 2 are significant (Rule #1)
                - the 2 zeroes between them are significant

3. Any zero before the first non-zero is not significant.
Ex.
      0.102 has 3 significant figures: 0.102 
          - 1 and 2 are significant (Rule #1)
               - the zero between the 1 and 2 is significant (Rule #2)
               - The first zero is not significant because it comes before the first non-zero.    
     
      0.00012 has 2 significant figures: 0.00012
           - 1 and 2 are significant (Rule #1)
               - All of the zeroes are before the first non-zero and are not significant

4. Any zero after a non-zero with a decimal point is significant.
Ex.
      1.0 has 2 sig figs: 1.0 
          - the 1 is significant (Rule #1)
               - the 0 is significant because there is a decimal     

     1.2030 has 5 sig figs: 1.2030 
          - the 1,2, and 3 are significant (Rule #1)
              - the first zero is between two non-zeros and is significant (Rule #2)
              - the last zero is after the last non-zero and there is a decimal point.

5. Any zero after a non-zero without a decimal point is not significant.
Ex.
      10 only has 1 sig fig: 10
         - 1 is significant (Rule #1)
              - there is no decimal point     
  
     1010 has 3 sig figs: 1010 
         - 1 is significant (Rule #1)
             - the first zero is between two non-zeros (Rule #2)
             - the last zero is not accompanied by a decimal and is therefore not significant.

Adding and Subtracting
When you add or subtract numbers the answer should be rounded to the lowest number of decimal places.

Steps:
1) Add or subtract as the problem states.
        12.03 + 1.9 = 13.93

2) Identify # of decimal places
        12.03 + 1.9 = 13.93Ex.
             2 dp          1dp 

3) Identify lowest number of decimal places
        1.9 has only 1 decimal place

4) Round answer to match the lowest number of decimal places
       Since the lowest number of decimal places is 1 my answer can
       only have 1 decimal place.
      13.93 is rounded to 13.9.

5) Correct Answer: 13.9

      2.5233 - .125874 = 2.397426
          4 dp                6dp               2.3974 is the correct answer    
   
      35.63 + .2586 = 35.8886
        2 dp             4 dp         35.89 is the correct answer

Multiplication and Division
When you multiply or divide numbers the answer should be rounded to the lowest number of significant figures.

Steps:
1) Carry out multiplication or division as usual.
      12 x 30 = 360

2) Identify numbers of significant figures.
     12 has 2 sig figs (Rule #1)
     30 has 1 sig fig (Rule #1 and #5)

3) Identify lowest number of sig figs
     30 has 1 sig fig which is the lowest number of sig figs

4) Round the answer to the lowest number of sig figs.
    360 has 2 sig figs (Rule #1 and #5) and will round to 400 to match 1 sig
    fig.

5) Correct Answer: 400

Ex.
      30560 x 101 = 3086560
       4 sig figs      3 sig figs    3090000 is the correct answer
         (R #1,2,5)   (R #1,2)     
 
      65 / 200 = 0.325
      2 sf      1 sf         0.3 is the correct answer
      (R#1)    (R#1,5)   *Note that the 2 and 5 are not turned to 0s like in the first example. These zeroes
                                                  would be significant based on Rule #4 and would give the answer 3 sig figs.

Websites:
                      
Replacement Assignment print this out and turn it in on Tuesday, September 6. If you are using it to replace Significant Figures Homework on Page 10 it must be turned in on Tuesday. If you are using it as extra credit you have until Friday.

Click here for an awesome explanation of rules with great examples.