1. Significant Figures

2. Why Significant Figures
 It enables us to have a clear idea of the
extent of the precision of the measuring
instrument being used or the measuring
method being employed.

3. Which figures are significant?
 Rule #1: Non-zero
digits are always
significant
 Rule #2: All zeroes
between significant
digits are significant
 Rule #3: A final zero
or trailing zeroes
can only be
significant if there is a
decimal point or a
bar.
Let’s practice!
1234 kg
56, 789 ft
101 hr
134.001 kW
1230909 cm
10.0 s
100. s
$ 2050.00
7000 kW
0.0204000

4. Which figures are NOT
significant?
 Zeroes are usually not significant in
the following instances:
 Leading zeroes: zeroes before any
significant figure are never significant.
 Ex. 0056, 0.00108
 Trailing zeroes: zeroes after any
significant figure are not significant
when there are no decimal points or
bars
 Ex. 76 000, 76 000., 76 00.0, 0.076000, 76

5. Infinite Number of Significant Figures
 Counted Numbers
 12 eggs in a dozen
 There are 16 students in a class
 Physical Constants
 The value of π (3.14)
 Avogadros’ Constant 6.02 x 1023

6. Seatwork: How many significant figures?
1. 600.
2. 2.090
3.
4.
5.
6.
0
3045
0.001
0
0.056
0
0.009
9
8. 0.0300
9. 0.0080
10.10
006
11.0.003
30
12.0.070
0
13.2 900

7. Seatwork: How many significant figures?
•
•
•
•
•
•
•
20.005
5.0900
5 000
3.006
7.0809
0.0350
31.670
• 0.0400
4
• 123.45
0
• 103.05
• 60.00
• 200.0
• 0.0070
0

8. How many significant figures are in the
following measurements?
1. 30.0
2. 239
3. 0.890
4. 43.20
5. 1000
6. 34.42
7. 90.0
8. 0.0021
9. 5.400
10.0.0023
11.14.60
12.2 050
13.200.60
14.35
15.136.04
16.980.00
0
17.3.
18.570.0
19.0.700
20.12.040
21.460.13
22.15.010
23.19.80
24.0.0400
1

9. Adding and Subtracting
 The result must be
rounded off to have
the same number
of decimal places
as the quantity with
the least number of
decimal places.
Examples:
 0.0836 + 195.2 =
195.3
10.00
 2.67 + 7.3333 =
 3.5212 – 3.12 =
0.40
 6 – 0.384 =6

10. Multiplying and Dividing
 The result must be
rounded off to have Examples:
6.53
0.0390
the same number  0.0620 × 105.30 =
of significant
500
 3.000 × 0.0130 =
figures as the
 1000. / 2.010
=
quantity with the
 9 / 0.765 =
least number of
significant figures.

11. Practice Work.
1.
2.
3.
4.
5.
6.
7.
8.
37.76 + 3.907 + 226.4 = ?
319.15 - 32.614 = ?
104.630 + 27.08362 + 0.61 = ?
125 - 0.23 + 4.109 = ?
2.02 × 2.5 = ?
600.0 / 5.2302 = ?
0.0032 × 273 = ?
3
(5.5) = ?

12. Practice Work.
1. 37.76 + 3.907 + 226.4 = 268.1
2. 319.15 - 32.614 = 286.54
3. 104.630 + 27.08362 + 0.61 = 132.32
4. 125 - 0.23 + 4.109 = 128.879 ~ 129
5. 2.02 × 2.5 = 5.05 ~ 5.1
6. 600.0 / 5.2302 = 114.7183364 ~
114.7
7. 0.0032 × 273 = 0.8736 ~ 0.87
3
8. (5.5) = 166.375 ~ 170

13. Practice Work.
9. 0.556 × (40 - 32.5) = ?
10. 45 × 3.00 = ?
11. What is the average of 0.1707,
0.1713, 0.1720, 0.1704, and 0.1715?
5
2
12. 3.00 x 10 - 1.5 x 10 = ? (Give the
exact numerical result, and then express
that result to the correct number of
significant figures).