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Significant Figures
Why do we need to know significant
figures?
 We as scientists need to measure things as we
perform experiments.
 Instruments have different degrees of
precision
 We measure to the last known calibration, and
estimate the unknown.
Significant = replaceable
 A number is significant because it can be
replaced by another number in a
measurement
The Rules
Significant Figures – The Rules
 1. Nonzero numbers 1 – 9 are always
significant.
 Examples:
 1 meter
1 sig fig
 92 liters
2 sig figs
 34578 grams 5 sig figs
Significant Figures – The Rules
 2. Imbedded zeros (zeros between nonzero
numbers) are always significant.
 Examples:
 202 cm
 10509 mL
 2039 kg
 90009 g
3 sig figs
5 sig figs
4 sig figs
5 sig figs
Significant Figures – The Rules
 3. Leading zeros are never significant.
 4. Trailing zeros after a nonzero number
after the decimal are significant.
 Examples:
 0.00000540 g
 0.3700 mm
 0.00101 L
3 sig figs
4 sig figs
3 sig figs
Significant Figures – The Rules
 5. Trailing zeros before the decimal are
significant only if the decimal point is
specified.
 Examples:
 100. dg
 100 dg
 8900 km
 8900. km
3 sig figs
1 sig fig
2 sig figs
4 sig figs
Exact Numbers
 An exact number is a number that cannot be
changed. (Cannot be halved or split up)
 Ex. 2 atoms, 1 proton, a hundred dollar bill
 We include most conversion factors as exact
numbers
 Ex. 1m = 100 cm
 When you work with exact numbers, you
consider them to have infinite sig figs.
(You don’t have to worry about them!)
RECAP #1
Leading Zeros
Imbedded Zero
0.00770800
Nonzero numbers
Trailing Zeros
after the decimal
6 significant figures
RECAP #2
Leading Zeros
(none)
Imbedded Zero
22060
Nonzero numbers
Trailing zero
with no decimal
4 significant figures
Lets Practice!
56 meters
2 sig figs
Rule 1
20 grams
1 sig fig
Rule 1, 5
303.0 mL
4 sig figs
Rule 1, 2, 4
200 dollars
1 sig fig
Rule 1, 5
207 donkeys
3 sig figs
Rule 1,2
0.7900 grams
4 sig figs
Rule 1,3,4
0.0096070 m
5 sig figs
Rule 1,2,3,4
102000 km
3 sig figs
Rule 1,2,5
1.10 x
2
10 hm
3 sig figs
Rule 1, 4
2.2 x
34
10
atoms
2 sig figs
Rule 1
Rounding Numbers
 If you have to round and the number you
are looking to round is less than 5, don’t
round.
 Example:
214
round to 2 s.f.
Answer = 210
Rounding Numbers
 If you have to round and the number you
are looking to round is 5 or greater, round
up.
 Example:
215
round to 2 s.f.
Answer = 220