Sig Figs
Easy as…
IDing Sig Figs
Significant Figures
•
All the digits used to report a
measurement including the
uncertain digit (your guess).
• The only digits that are NOT
considered significant are zeros that
are present simply as placeholders.
Rules to help decide which
digits are significant
1. All non-zero numbers in a measurement
are significant. (Ex: 1, 2, 3 ect)
2. Zeros are significant only if they:
a) are surrounded by other significant figures.
Sandwiched in between
(ex. 120,001m)
b) appear at the end of a decimal number. (ex.
3.940)
c) have a bar over them. (ex. 6,32Ō KJ)
Examples
• How many significant figures are in
23,457.12km?
• Rule 1 – All non-zero numbers are
significant. Therefore there are 7
significant figures.
• How many significant figures are in
98,001g?
• Use Rule 1 and 2a – Zeros are
significant if they are surrounded by
other significant figures. Therefore
there are 5 significant figures.
More Examples
• How many significant figures are in
2.3100s?
• Use Rules 1, 2a, and 2b – Zeros at the end of
a decimal number are significant. There are
5 significant figures.
• How many significant figures are in
57ŌŌ00 nm?
• Use rules 1, 2a, 2c – Zeros with a bar over
them are significant. Therefore the last 2
zeros are NOT significant. There are 4
significant figures
One More Example
How many significant figures are in
0.0030160L?
• Use rules 1, 2a, and 2b. The first 3 zeros do
NOT fit any rules, therefore there are 5
significant figures.
Figuring Significance
• Figuring Significance
• Indicate the number of significant figures in each of the
following numbers.
1. 3,409 kg
4
7. 490,050 mm
5
2. 0.007014 L
4
8. 15,003.030 s
8
3. 84,000.0 Ω
6
9. 560,Ō00 L
4
4. 0.00034050 cm
5
10. 345,000 kg
3
5. 10 L
1
11. 0.000000003 km
1
6. 1,430,000 s
3
12. 0.00743 m
3
Significant Measurements
•
Look at the scale to the right
and record the measurement in 6,000 L
the space below.
A. 5,880 L
• How many significant figures
does the measurement have?
Explain your answer.
A. 3, The last zero is
not significant
• Assume there is another arrow
pointing exactly at the 6,000 L
mark, how would you report the
measurement so that you have
the correct number of
significant figures?
A. 6,0 0 0 L
5,000 L
Exact or Counted Numbers
• Significant figures only apply to
measurements when there is an uncertain
digit.
• Counted numbers are perfectly exact and
do not have uncertainty. They have an
infinite number of significant figures.
• Example: 12 eggs could be
12.0000000…eggs (a dozen always means 12
no matter what your
talking about)
Rounding and Rule of 5
Rounding Rules
• Always use the number to the right of the
number you are rounding to.
• 1, 2, 3, 4 always round down:
So 3.3 rounds to
3
•
6,7,8, and 9 always round up :
So 4.7 rounds to
5
Rule of 5’s
• 5 will round a number up
• Examples
 Round 4.85 to 2 sig figs
• 4.9
 Round 7.335 to 3 sig figs
• 7.34
Let’s Review
• 4.5 rounds to
5
•
3.5 rounds to
4
•
2.57 rounds to
3
•
2.5000001 rounds to
3
Measurements used in calculations
• When measurements are used in calculations
the answer cannot be any more accurate than
the original measurements.
• Example: Rectangle with a width of 1.8 cm and
a length of 4.3256 cm. What is the area?
•
Multiplying gives you 7.79608 cm.
•
You can only have 2 significant figures.
Therefore the answer is
7.8 cm.
Practice
• Round the following numbers to four significant
figures.
23,005.1 g
2.78320 g
0.0089345 L
201,455 m
• Round the following numbers to five significant
figures.
872,345 g
0.00435671 s
200.0651 cm
0.0987335 g
Multiplication and Division
Multiplication and Division
• The answer should contain the same number
of significant figures as the measurement
with the least number of significant figures
•
•
3 Sig Figs
5 sig figs
Example: (4.56 mm) (3.4624mm) =
3 sig figs
3 sig figs
3 sig figs
15.788544
mm2
 15.8 mm2
2 sig figs
Example: (3.45m) (6.24m) (2.0m) =
43.0560
m3

2 sig figs
43 m3
Adding and Subtracting
Addition and Subtraction
• The answer must be rounded to the last
decimal place of the least accurate
number.
• Example:
•
3.23m
+ 154.2 m
•
157.43 m
• The correct answer should be…
157.4m
Examples
• Example:
•
17,000m
-
•
6,430m
10,570m
• The correct answer should be…
11,000
since the least accurate measurement is
17,000 with uncertainty in the thousands
place.
Adding to Your Significance
Solve the following math problems, reporting your answers to the
correct number of significant figures. Indicate the uncertain
figure in each number by underlining it. Be sure to also show
the pre- and post rounded numbers.
Initial Answer
Rounded
with correct
sig figs
1. 34.8 nm + 22.45 nm =
57. 25 nm

57.3 nm
2. 3.67 kg – 3.62 kg =
0.05 kg

0.05 kg
3. 7.39 m + 3.467 m
+ 1.0 m – 8 m =
3.857 m

4m
Mixed Problems
Mixed Problems
• Follow the Order of Operations
• PEMDAS
 Please Excuse My Dear Aunt Sally
•
•
•
•
2
•
Parentheses
Exponents and Roots
Multiplication and Division
Addition and Subtraction
4
2
3
EX: (23 cm+1.435 cm) (450 cm) / (16.3 cm) =
 SHOW YOUR WORK!!!
(24.435 cm x 450 cm) / (16. 3 cm)
= 674.58588957
= 670 cm
Significant Operations
•
Solve the following math problems, reporting your answers to
the correct number of significant figures. For addition or
subtraction, indicate the uncertain figure in each number by
underlying it. For multiplication and division, indicate the
number of significant figures in each number by placing a
small number above each measurement. Be sure to also show
the pre- and post rounded numbers.
3
3
2
1. (176 m)(325 m)(1.2 m) =
=68,640m3
(2 sig fig)
=69,000m3
2
4
1
3
2. (0.0000023 cm)(1.435 cm)(7,000 cm) / (122 cm) =
= 0.000189373cm2
(1 sig fig)
0.0002cm2
Significant Operations cont
9
3.
6
(1.33490001 m)(16,000.0 m) =
= 21358.40016m2
(6 sig fig)
= 21,358.4m2
4
4.
3
(1.948m) / (2.43s) =
= 0.801646091 m/s
(3 sig fig)
= 0.802 m/s
3
4
2
5
5. (0.663 kg)(4.391 m) / [(3.2 s)(9.1000 s)]
= 0.009997366 kg m/s2
(2 sig fig)
=0.010 kg-m/s2