Significant Figures
How to determine and use the proper sig.
figs.
What is a significant
figure?
 There
1)
2)
are 2 kinds of numbers:
Exact numbers
Measured numbers
What is a significant
figure?
1) Exact: don’t come in
fractions or decimals!!!
 Ex:
humans
 Ex: bacterial
colonies on a petri
dish
What is a significant
figure?
On
the other hand…not
everything is so
easy…sometimes you have
to …
Approximate: A close guess
that is in the ball park.
When to use Significant
figures
2) Measured numbers
Using a tool/ device to measure…you
must ask yourself what are the limits
of the tool/ device.
 Ex:

When to use Significant
figures
 You
could
measure Arrow
“A” as 3.9cm.
But to some
mathematicians
3.9cm, or
3.90cm is the
same.
A
Key difference
 But,
to a scientist 3.9cm and
3.90cm is NOT the same
Uncertainty
The limit of the device!
Uncertainty is defined as ½ of the smallest certain unit
If a Centimeter Ruler was used…
A
B
Arrow
Length ± 0.5cm*
Arrow “A”
3.9
Arrow “B”
3.4
*You should report the uncertain digit
If a Millimeter Ruler was used…
Arrow
Length ± 0.5mm*
Arrow “A”
39.1
Arrow “B”
33.8
Uncertainty
The limit of the device!
Uncertainty is defined as ½ of the smallest certain unit
What about electronic devices?*
Digital Balances:
The last digit is uncertain.
For example: The mass of the
powder is 5.00g ± 0.05
*some electronic devices have published uncertainty,
If you have access to the manual, refer to it.
How do I know how many Sig
Figs?
 Basic
Decimal Rules
If no Decimal, then start counting at the
first NON zero, and stop counting at the
last NON zero!
 30

1 sig fig
 303

3 sig figs
 3030 
3 sig figs

How do I know how many Sig
Figs?
 Basic
Decimal Rules
If Decimal, then start counting at the
first NON zero, and count until the end!
 3.1

2 sig fig
 3.03 
3 sig figs
 3.030 
4 sig figs
 0.303 
3 sig figs

How many sig figs?
7
1
40
1
0.5
1
0.00003
1
7
5
10
x
7,000,000
1
1
How many sig figs here?
 1.2
2
 2100
2
 56.76
4
 4.00
3
 0.0792
3
 7,083,000,000
4
Identify the uncertain
digit in each number?
 1.2
 1.2
 2100
 2100
 56.76
 56.76
 4.00
 4.00
 0.0792
 0.0792
 7,083,000,000
 7,083,000,000
How many sig figs here?
 3401
4
 2100
2
 2100.0
5
 5.00
3
 0.00412
3
 8,000,050,000
6
How would you indicate
uncertainty?
 3401
 2100
 2100.0
 5.00
 0.00412
 8,000,050,000
 3401
±5
 2100 ±500
 2100.0 ±0.5
 5.00 ±0.05
 0.00412 ±0.00005

8,000,050,000 ±50,000
What about calculations with sig
figs?
 Rule:
When adding or
subtracting measured numbers,
the answer can have no more
places after the decimal than the
LEAST of the measured
numbers.
Add/Subtract examples
 2.45cm
+ 1.2cm = 3.65cm,
 Round off to
= 3.7cm
 which digit is uncertain?
 3.7
Add/Subtract examples
 7.432cm
+ 2cm = 9.432 round
 9cm
to
 which
9
cm
digit is uncertain?
Multiplication and Division
 Rule:
When multiplying or
dividing, the result can
have no more significant
figures than the least
reliable measurement.
A couple of examples
cm x 2.45cm = 139.111 cm2
 Round to
 139cm2
 which digit is uncertain?
 56.78
 139
cm2
A couple of examples
75.8cm
x 9.6cm = ?
Do the math and round to…
 Which digit is uncertain?
 How would you record uncertainty?

Sig fig Math!!!