Transcript Slide 1
Applied Mathematic
(Preliminary General 1)
Significant
Figures etc
Stage 6 - Year 11
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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
23