Powers That Be

1
Powers That Be
23 November 2009
Learning objective To understand indices and
standard form
Mr. Ws Daily News Report
We can happily announce the prize fund for
tonights lottery is 3 x 3 x 3 x 3 x 3 x 3 x 3
There has to be an easier way of saying this
number. What is it?
2
3 x 3 x 3 x 3 x 3 x 3 x 3
The calculation can be written using a BASE
number and an INDEX number
3
7
Index number
Base number
An index tells you how many times the base number
is multiplied by itself.
You would read this example as 3 to the power 7
8
12
9
5
4
2
6
6
8 to the power 4
12 to the power 2
9 to the power 6
5 to the power 6
3
Read These Indices
3
2
6
7
5
4
2
3
4
What is the index?
3
2 x 2 x 2
2
2
3 x 3
3
4
5 x 5 x 5 x 5
5
5
What do the following mean?
3
10 x 10 x 10
10
2
10 x 10
10
6
When we multiply by 10, the decimal point of a
number jumps 1 place to the right.
So what do you think will happen to a decimal
place when we times by 10 ?
2
Well if the decimal point moved 1 place when we
times by 10, 10 means 10 x 10 the decimal point
will then move twice.
2
7
How many times do you think the decimal point
will move in the following questions
3
3
8.1 x 10
times
8
8
4.9 x 10
times
8
To write a number using a power of 10 is
important when it comes dealing with certain
types of numbers. This is otherwise known as
standard form. But what is standard form and when
would you use it?
To write a number using a power of 10 is
important when it comes dealing with certain
types of numbers. This is otherwise known as
standard form. But what is standard form and when
would you use it?
Lets look to the stars!
9
These are some of the planets in our solar
system.
They tend to vary in size
For example.
10
(No Transcript)
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As you can see, stars can be bigger than planets
12
A lot bigger
13
A lot, lot bigger
14
It can be difficult to make sense of space due to
its size. Mathematics is very important not only
in helping to understand, but also to make
calculations in order to answer the many
questions that are still mysteries.
15
The distance between earth and the sun is roughly
150, 000, 000km
With astronomy it is good to use standard form
since the distances astronomers use are so large.
To write a number in standard form the first
number needs to be between 1 (inclusive) and 10,
multiplied by a power of 10
16
The distance between earth and the sun is roughly
150, 000, 000km
So to make the number above to be a number
between 1 and 10, a decimal point needs to be
placed between the 1 and 5.
How many times would the decimal point need to
move to get back to its original place?
Notice, standard form reduces the need to have
all the zeros in a very large number
1.5
x 10
1.50000000
8
Count it.
8 times to the right
What would you multiply this number by to make
the decimal point move 8 places to the right?
8
10
17
Standard Form Problems

• 1) Write the diameter of these stars in standard
  form
• The Sun 1,392,000 km
• Arcturus 34,079,500 km
• Antares 970,370,000 km
• 2) One light year 6,000,000,000,000 miles
• Write this number in standard form
• 3) The distance to the Sun from the Earth is 9.35
  x 107
• Write this number out in full.

6
1.392 x 10
3.40795 x 10
7
8
9.7037 x 10
12
6.0 x 10
93, 500, 000