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Scientific Notation

What is a scientific notation. Where we use it. How we use it.
by

Rebeka Wojcicka

on 2 September 2013

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Transcript of Scientific Notation

And where we use it
What is a
Scientific Notation?
And 100 000 000,
1 000 000 000, and 10 000 000 000
are just devastating.
How many zeroes that?

What about 100, 1000,
or 10000?
Still manageable is it?
100 000, 1 000 000,
and 10 000 000 are
the tricky ones, especially
when you want to put
them into your
calculator

is
And that's
when Scientific
Notations step up
to make your life a
hundred times
easier!
It's not just
huge numbers
that a Scientific
Notation helps with,
it helps with tiny numbers
too! Like:
0.0001, 0.00001,
0.000001 0.0000001
0.00000001,
0.000000001,
0.0000000001,
0.00000000001,
0.000000000001,
and
0.0000000000001
How do we
calculate them?
Scientific Notations look like this
2 x10
5 x10
8.1 x10
3.85 x10
or sometimes
6e9
9.2e4
7.13e6
-11
-3
5
8
If the number is more complicated
remember this formula

n x10
j
n= number
this number must always be higher than 0, and less
than 10 (it cannot be 0 or 10 but it can be a
decimal)
j
= jumps from the old decimal
to the new
How to calculate the
Scientific Notation of
250 000 000
1. Figure out where the decimal is. In this case it would be 250 000 000
.
2. Figure out what is the number that that is
going to go in front of the x10
Remember: it has to be >0 and <10
That number would be 2.5
3. Replace the n in n x10 with
the number selected in the previous step.
The formula now is 2.5 x10
4. Calculate what
j

is. How many
jumps
are there from the old decimal to the
new one?
2 5 0 0 0 0 0 0 0
.
.
new decimal
old decimal
j
j
8
So the Scientific Notation
form of
250 000 000
is
2.5 x10
8
You calculate very
small numbers in the
same way, the only difference is the minus sign that you have to put in front of the Scientific Notation power
e.g.:
0.000000025
would be
2.5 x10
-8
Where is Scientific Notation used?
How small is an 'atom'?

0.0000000001
metres

1 x10
metres
-10
Small Numbers:
How long does it take for light to
travel one metre? Aproximately*

0.000000003335
seconds

3.335 x10
seconds
-9
Small Numbers:
*exactly 3.335640952 x 10
-9
If you get $5 pocket money for
a week, on average how many
dollars do you get per second?

0.0000083
dollars

8.3 x10
dollars
-6
Small Numbers:
$5 divided by 7 days
divided by 24 hours
divided by 60 minutes
divided by 60 seconds
equals

0.0000083
dollars

8.3 x10
dollars
-6
How did I get that?:
How many years does it take for
a snail to go 1mm?

0.0000000317
years

3.17 x10
years
-8
Small Numbers:
What is the volume of a single
pebble measured in cubic meters

0.00000003351
cubic meters

3.351 x10
cubic meters
-8
Small Numbers:
How many stars are there in
our galaxy? Roughly

200 000 000 000
stars

2 x10
stars
-11
Big Numbers:
How heavy is planet Earth?

5 970 000 000 000 000 000 000
tons

5.97 x10
tons
21
Big Numbers:
How many liters of water is on
the surface of Earth? About

1 260 000 000 000 000 000 000
liters

1.26 x10
liters
21
Big Numbers:
How fast does a Space Shuttle
travel?

27 000 000
meters/hour

2.7 x10
meters/hour
7
Big Numbers:
On avarage, how many blinks
are there on Earth per day?
(Counting all the people on Earth)

108 500 000 000 000
blinks/day

1.085
blinks/day
14
Big Numbers:
What is it?
A scientific notation
is just a different way of
writing a number that is extra big or microscopically tiny
Why
'Scientific' Notation?
There is really little
scientific abut a
'Scientific' Notation, it's all numbers, but these notations
are mainly used
in science and maths
Why
do we use them?
If you have a number like
5 or 13, It's relatively easy to
use, write, and understand
Where is Scientific Notation used?
With simple numbers like

300 000 000
where there is one digit that is not a zero, all
you do is count the number of zeroes after the number.
In this case there are 8 zeroes, so remove them
from the end leaving the single digit at the
front and put the number of zeroes as
the power, making
3 x10
8
18
The person who invented chess asked the King to put one grain
of wheat on the first chess square, doubling the amount or grain for every square







How many grains should have been on the last square?
9 223 372 037 000 000 000

9.223372037 x10
Big Numbers:
1 2 4 8 16 32 ....
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