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?

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

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 ....