Significant Figures
• A significant figure (sig fig) is a measured or
meaningful digit
• Sig figs are made of all the certain digits of a
measurement plus the first uncertain digit
(the extra digit you had to guess remember?)
Significant Figures
1. Non-zeroes are significant
2. Zeroes between sig figs are significant
- e.g. 101 (3), 10001 (5)
3. Zeroes at the end of numbers without
decimals are not significant
- e.g. 10 (1), 100 (1), 1100 (2), 10400 (3)
Significant Figures
4. Zeroes at the end of numbers with decimals
are significant
- e.g. 100.0 (4), 1.00 (3), 1.0000 (5)
5. Zeroes in front of numbers with decimals are
not significant
- e.g. 0.01 (1), 0.010 (2), 0.0000100 (3)
Practice
• Hebden p.37 #55
Problem with Rule #3
• How can we express 10,000 as 5 sig figs if the
zeroes at the end are not significant?
Problem with Rule #3
• How can we express 10,000 as 5 sig figs if the
zeroes at the end are not significant?
• The bad way: add a decimal at the end
10,000.
• Do not do this in Chem 11…or ever
• But you still need to recognize they mean 5 sig
figs when that’s written
Problem with Rule #3
• How can we express 10,000 as 5 sig figs if the
zeroes at the end are not significant?
• The good way: use scientific notation
(exponents)!
Problem with Rule #3
• How can we express 10,000 in 5 sig figs if the
zeroes at the end are not significant?
• Use scientific notation (exponents)!
• 10,000 = ? x 10?
Problem with Rule #3
• How can we express 10,000 in 5 sig figs if the
zeroes at the end are not significant?
• Use scientific notation (exponents)!
• 10,000 = 1.0000 x 10?
Problem with Rule #3
• How can we express 10,000 in 5 sig figs if the
zeroes at the end are not significant?
• Use scientific notation (exponents)!
• 10,000 = 1.0000 x 104
Problem with Rule #3
• How can we express 10,000 in 5 sig figs if the
zeroes at the end are not significant?
• Use scientific notation (exponents)!
• 10,000 = 1.0000 x 104
• Rule #4: Zeroes at the end of numbers with
decimals are significant
Scientific Notation
• When you move a decimal right, you must
multiply by 0.1
0.00054321 = 5.4321 x 0.1 x 0.1 x 0.1 x 0.1
= 5.4321 x 10-1 x 10-1 x 10-1 x 10-1
= 5.4321 x 10-4
• When you move a decimal left, you must
multiply by 10
12345 = 1.2345 x 101 x 101 x 101 x 101
= 1.2345 x 104
Standard Notation
• These are the “regular” numbers without the
exponents (the opposite if you will)
• You need to know how to convert b/t the 2
• Positive exponent: move decimal right
– 3.385x102  338.5
• Negative exponent: move decimal left
– 3.385x10-2  0.03385
Practice Conversions
• Express the following in scientific notation
0.0002734
12386.93
10.124
• Express the following in standard notation
7.002 x 10-3
1.63 x 102
0.01284 x 10-2
Rounding
• Some of us are used to always rounding 5s up
– E.g. 20.5  21
• In Chem 11, we will round 5s to the nearest
even number
– E.g. 20.5  20
– E.g. 21.5  22
(20 is nearer than 22)
(22 is nearer than 20)
Arrow Rule for Sig Figs
• If there is decimal: arrow starts from the left
0.000345490
0.000345490
6 sig figs
• If no decimal: arrow starts from the right
175450400 
175450400
7 sig figs
• Arrow moves until it hits a non-zero
• Count the numbers that are left when the
arrows stops and those are your sig figs
• 4 or 5 volunteers to help demonstrate please
Arrow Rule for Sig Figs
•
•
•
•
Form 4 lines
Inside lines face out, outside lines face in
Each line is a team
One team makes up a number while the other
team uses the arrow rule to determine the
number of sig figs in that number
• Switch roles after 1 person answers
• Everyone must answer at least once
Arrow Rule for Sig Figs
•
•
•
•
Use the cards I’ve given to make numbers
Move around to change the order
Can hold 0, 1 or 2 cards in your hands
Hold them up and show the other team when
you’re done so they can answer
• Tally up scores and the winners can go against
each other
Arrow Rule for Sig Figs
• +1 point for every correct answer
• -1 point for every “bad” number made up
E.g.
0001204.0
184.
0.475.380
• Try to let the arrow figure it out themselves
• Remember: it’s not about the outcome, it’s
about the process
Homework
• Sig figs worksheet #1 and 5
Calculations Using Sig Figs
Multiplication & Division
• Round the answer to the least number of sig
figs contained in the question
• 2.391 x 4.5 = ?
Multiplication & Division
• 2.391 x 4.5 = ?
Multiplication & Division
• 2.391 x 4.5 = ?
• 4 sig figs x 2 sig figs = ?
Multiplication & Division
• 2.391 x 4.5 = ?
• 4 sig figs x 2 sig figs = ?
• 4 sig figs x 2 sig figs = 2 sig figs
Multiplication & Division
• 2.391 x 4.5 = ?
• 4 sig figs x 2 sig figs = ?
• 4 sig figs x 2 sig figs = 2 sig figs
• 2.391 x 4.5 = 10.7595
Multiplication & Division
• 2.391 x 4.5 = ?
• 4 sig figs x 2 sig figs = ?
• 4 sig figs x 2 sig figs = 2 sig figs
• 2.391 x 4.5 = 10.7595  11 (2 sig figs)
Multiplication & Division
• Practice: Hebden p.39 #56
Addition & Subtraction
• Round off the answer to the least precise
number in the problem
• Remember that least precise means fewest
decimal places
Addition & Subtraction
• 29.347 + 2.33 = ?
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = ?
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = 2 decimals
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = 2 decimals
• 29.347 + 2.33 = 31.677  round to 2 decimals
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = 2 decimals
• 29.347 + 2.33 = 31.677  round to 2 decimals
• 29.347 + 2.33 = 31.68  2 decimals, 4 sig figs
Addition & Subtraction
• 2.45 x 105 + 3.1 x 104 = ?
• Must convert to the same exponent to see
which is less precise
• Always convert the smaller exponent into the
larger one
Addition & Subtraction
• 2.45 x 105 + 3.1 x 104 = ?
• 2.45 x 105 + 0.31 x 105 = ?
Addition & Subtraction
• 2.45 x 105 + 3.1 x 104 = ?
• 2.45 x 105 + 0.31 x 105 = ?
• 2.45 x 105 + 0.31 x 105 = 2.76 x 105
Practice
• Hebden p.28-34 #42-50, p.37 #55 (was HW)
• Add/subtract: Hebden p.40 #57
• All operations: Hebden p. 40 #58-59
• Hand in sig figs worksheet (online).