Indices and standard form
Transcript of Indices and standard form
Indices and Standard Form
Slide 1Chapter
10
It’s 144 000 000 km,
or 1.440 00 x 108 km.
or 1.440 00 x 100 000 000 km,
Earth to Moon: 384 835 km
Earth to Sun: 144 000 000 km
We know that the Sun is very far from the Earth. But how far exactly is it? How many digits are needed to represent this distance?
What about the distance from the Earth to the Moon?
Indices and Standard Form
Slide 2Chapter
10
Moon:
7.3 x 1019 metric tons
Sun:
22 x 1027 metric tons
Earth:
6.6 x 1021 metric tons
Besides the distances mentioned earlier, even the masses of the Earth, the Moon and the Sun are pretty large too.
The numbers involved are so large that we make use of INDICES to represent them.
Indices and Standard Form
Slide 3Chapter
10
Diameter of a human hair: 0.000 025 4 m
We can rewrite it as
25.4 x 0.000 001 m,
or 25.4 x 10-6 m
Besides representing very large numbers, we can also make use of INDICES to represent very small numbers.
Some examples: diameter of a strand of hair, size of an atom, size of a bacterium
What are INDICES then?
Indices and Standard Form
Slide 4Chapter
10
1.440 00 x 108 km 25.4 x 10-6 m
These numbers are called INDICES.
We make use of INDICES to represent extremely
LARGE or small numbers.
INDICES saves us from writing long string of
digits, saving time and effort, and reducing the
chance of missing out digits.
Indices and Standard Form
Slide 5Chapter
10
22 x 1027
= 22 000 000 000 000 000 000 000 000
Imagine having to write out 22 x 1027 which is the value of the mass of the Sun, in full in your assignment about the Solar System.
Indices and Standard Form
Slide 6Chapter
10
23
2 x 2 x 2 can be written as 23,
where Index / Exponent
Base
Indices and Standard Form
Slide 7Chapter
10
a5a3 x aa x a x a x aam = x aa x a … a
m times
x aa x a
Indices and Standard Form
Slide 8Chapter
10Below are the laws of indices for expressions with a common base.
amx an = am+n
am an = am-n
(am)n = am n
Indices and Standard Form
Slide 9Chapter
10
Summary
amx an = am+n
am an = am–n
(am)n = am n = amn
Indices and Standard Form
Slide 10Chapter
10
a3
=x
(ab3
(a (a b) b) b)x=
(a) (a) (a)
(a b)3
=
(b) (b) (b)
Below are the laws of indices for expressions with a common index.
Indices and Standard Form
Slide 11Chapter
10
=(a) (a) (a)
(b) (b) (b)
a3
b3
=
a
b
a
b
a
b
a
b
a
b
a
b
3
Indices and Standard Form
Slide 12Chapter
10Summary
amx bm = (ab)m
am bm = ( )ab
m
Indices and Standard Form
Slide 13Chapter
10
2-3
a0 = 10
a-n =
=n√a2
2√4
3√82
18123
1an
a1n41 281 3
Zero Index
Negative Index
Fractional Index
Indices and Standard Form
Slide 14Chapter
10
=n√a2
3√8a
1n81 3
a n =n√a
4
1 mm
8 3 =3√
1 22648
More on Fractional Index
Indices and Standard Form
Slide 15Chapter
10Summary
a0 = 1
a-n =1
an
= n√aa
1n =
n√ama
mn
Indices and Standard Form
Slide 16Chapter
10
4x 16= 42
2x
Equations Involving Indices
=
Indices and Standard Form
Slide 17Chapter
10
1.440 00 x 108
km
Index(plural: indices)Earth to Sun:
Then what is this form of expressing numbers known as?
1.440 00 x 108
A, where 1 ≤ A < 10 n is an integer.In general, A x 10n
— standard form of 144 000 000
Indices and Standard Form
Slide 18Chapter
10
Standard form for very large numbers
Yes! So, in standard form:
1.440 00 x 108
144 000 000 Numbers larger than 1,
move to the leftIs 1 ≤ A < 10 now?
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Indices and Standard Form
Slide 19Chapter
10Standard form for very small numbers
Yes! So, in standard form:1.440 00 x 10-7
0.000 000 144
Numbers smaller than 1,move to the right.
Is 1 ≤ A < 10 now?
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