Significant Figures
The Numbers Are Speaking to Me
5.689 cm
6.02 x 1023 bananas
45,000 L
Significant Figures
Numbers give two pieces of information
• The numerical value
• The degree of certainty
(more certainty = more digits)
Example:
5g
5 g measured to the ones place
(could be between 4.5 g and 5.5 g)

5.000g 5 g measured to the thousandths place
(could be between 4.9995 g and
5.0005 g)
Measurement
Measure as far as you can be certain
and then estimate one place further
We are certain that the reading is
between 30 and 40oC.
 3_ oC
We estimate that it is a little less
than half way.
 34oC
50
40
30
20
Decimal place depends on instrument used
Measure (in cm) to the correct number of significant figures.
5
6
7
8
7
8
6.83 cm
5
6
6.8 cm

We read the thermometer at the
right as 34oC. It is marked to the
tens place, so we estimate to the
ones.
50
40

How about now?
34.3oC

(marked to ones,
estimate tenths)
30
How about now?
40.0oC
(marked to ones,
estimate tenths)
20
Numbers
Significant does not mean important.
Significant means measured.
Rules
1) Non-zero numbers are significant.
95.357 g
5 SF
84.1 mL
3 SF
7 kg
1 SF
2) Zeroes between significant figures are significant.
308 m
3 SF
1.000004 g
7 SF
400.02 L
5 SF
3) Zeroes used for spacing are NOT significant.
Initial Zeros
0.0000567 g
3 SF
First Measured
Number
Zeros Holding
Decimal Place
Purely
Decorative
Final Zeroes
150
Last Measured
Number
2 SF
Zero Holding
Decimal Place
1,000,730,000
Zeros Between
Sigfigs
6 SF
Zeros Holding
Decimal Place
4) Final zeroes after a decimal point are significant.
7.300
4 SF
4.0
2 SF
150.00
5 SF
Zero between
Sigfigs
Final Zeroes
after Decimal
5) Zeroes between a sigfig and a decimal point are
significant.
150
2 SF
150.
3 SF
Lazy Principle – if it doesn’t change the mathematical
value, then it must have another purpose
6) Exact numbers (not measured) DO NOT
AFFECT sigfigs.
Counting
41 cars
23 students
45 tons of cars
infinite SF (Ø)
infinite SF (Ø)
2 SF
Conversions (by definition)
1 yard = 3 feet
infinite SF (Ø)
100 cm = 1 m
infinite SF (Ø)
Practice
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
456.01 mL
9,002 g
4,500 m
0.05 mg
25 lbs
17 pencils
0.000410 mol
4,000. yd


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


5 SF
4 SF
2 SF
1 SF
2 SF
infinite SF (Ø)
3 SF
4 SF
Scientific Notation
4.975 x 1041 m
Measured Digits
Decimal Place
The same as:
497,500,000,000,000,000,000,000,000,000,000,000,000,000
 4 SF
Only the measured digits affect sigfigs.