Significant Digits

1
Significant Digits

• The number of valid digits in a measurement.

2
Sig Figs

• The number of significant digits in a
  measuremennt is an indication of the precision
  with which a measurement was taken.
• How accurate is the measurement 186,000m?
• There is no way to tell. Are the zeros estimates
  or accurate measurements.

3
Sig Figs avoid confusion

• First way You can convert units to get rid of
  zeros.
• 186,000m can be converted to 186 km.
• Or, you can write it in scientific notation
• 1.86 x 105 m
• There are rules that determine the significance
  of a zero.

4
Sig Fig Rules

• All non zero numbers are significant.
• 135g has 3 significant digits.
• 1 m has 1 significant digit
• 123456789L has 9 sig figs.

5
Sig Figs cont.

• If a zero follows a decimal zero nonzero number
  and it is always significant.
• Ex. 1.00 m (3 sig figs)
• Ex. 123.0 km (4 sig figs)
• Ex. 0.00230 (3 sig figs)

6
Sig Figs cont.

• Zeros between 2 non zero numbers are significant.
  I call this the Oreo Rule.
• Ex. 1001 kg has 4 sig figs. (The ones are the
  cookies and the zeros are the cream filling.
• Ex. 10305 m has 5 sig figs.
• How many significant figures are in 12030405 km?

7
Sig Fig wrap up

• Zeros that are placeholders are not
  significant.
• Ex. 2200 km only has 2 sig figs.

8
Practice

• Do the following by yourself. Give the number of
  significant digits / figures in the following
  measurements
• A. 123.560 m
• B. 1004.5 km
• C. 12700 g
• D. 257 L

9
How do you know how many sig figs to use in your
answer?

• Look at the number of sig figs in your data.
• Choose the least number of sig figs and put your
  answer in this number of sig figs.
• Ex. V lxwxh
• V 1.2 x 2.33 x 4.5555 12.737178
• Answer will be in 2 sig figs 13