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Applied Mathematic
(Preliminary General 1)
Significant
Figures etc
Stage 6 - Year 11
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©G Dear 2010 – Not to be sold/Free to use
1
in the context of measurement.
We use these prefixes to help
with big numbers
2
in the context of measurement.
10 18
10 15
10 12
10 9
10 6
10 3
10 2
10
exa
E
peta
P
tera T
giga
G
mega M
kilo
k
hecto h
deka da
1 followed by 18 zeros.
1 followed by 15 zeros.
1 followed by 12 zeros.
1 followed by 9 zeros.
1 followed by 6 zeros.
1 followed by 3 zeros.
1 followed by 2 zeros.
1 followed by 1 zero.
3
in the context of measurement.
10 - 1
deci
d
0.1
10 - 2
centi
c
0.01
10 - 3
milli
m 0.001
10 - 6 micro
10 - 9 nano
10 - 12 pico
10 - 15 femto
10 - 18 atto
μ
n
p
f
a
0.000 001
0.000 000 001
0.000 000 000 001
0.000 000 000 000 001
0.000 (17 zeros) 001
4
Red
Team
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
6
101
kilo
10-3
10-1 10-15
M
5
tera
exa
10-12
T
102
atto
4
f
pico
1015
deci
da
1
3
10-18
giga

h
2
109
m
10-2
100
P
10-9
1
1018
103
nano
c
106
10-6
1
2
3
4
5
6
Blue
Team
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
24
23
22
21
20
19
18
5
Why use significant figures?
The distance from
the earth to the sun
is
240 757 786 km
A more meaningful distance would be …
241 000 000 km
3 significant figures is more meaningful.
6
Why use significant figures?
A stink bug is measured
with a micrometer.
as 0.025132 m
A more meaningful length would be …
0.025 m
2 significant figures
7
•All non-zero numbers are significant
2971
32.5
7.456
•zeros between non-zero digits are significant
3071
60.5
8.009
•zeros at the end of a decimal are significant
297.10
32.00
9.000
Practice
•all other zeros are not significant.
0900
0254
0.456
8
2.340
1
2
3
4
5
9
0.040
1
2
3
4
5
10
2340
1
2
3
4
5
11
120.34
1
2
3
4
5
12
2020
1
2
3
4
5
13
Why use scientific notation?
The distance from
the earth to the sun
is
241 000 000 km
In scientific notation it would be …
2.41 x 108 km
It’s easier with very large numbers.
14
Why use significant figures?
A stink bug is measured
with a micrometer.
as 0.025 m
In scientific notation it would be …
2.5 x 10-2 m
It’s easier with very small numbers.
15
(Also known as Standard Notation)
12 345
Write 354 000 in scientific notation.


How?
1. Move the decimal point from where it is 
to the standard position. 
(After the first non-zero number from the left.)
3.54 x 10?
2. How many places is it from the red arrow  to the
green arrow (where decimal point was)? +5
(with direction)
3.54 x 105
16
16
A
B
3.751x103 3751x103
A
B
C
D
3751x101 3.751x102
3751
C
D
17
A
9.1x103
A
B
9.1x104
B
C
91x103
91000
C
D
91x104
D
18
A
9.04x100
A
B
90.4x101
B
C
9.04x102
904
C
D
904x102
D
19
-3-2-1
Write 0.004 35 in scientific notation.


How?
1. Move the decimal point from where it is 
to the standard position. 
(After the first non-zero number from the left.)
4.35 x 10?
2. How many places is it from the red arrow  to the
green arrow (where decimal point was)? -3
(with direction)
4.35 x 10-3
AAmath
20
20
A
147x10-3
A
B
C
D
1.47x10-3 1.47x10-1 14.7x10-2
B
0.147
C
D
21
A
98x100
A
B
9.8x101
B
C
98x10-6
0.000098
C
D
9.8x10-5
D
22
A
3.4x10-4
A
B
3.4x10-3
B
C
34x10-3
0.0034
C
D
34x103
D
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