Scientific Notation

Shorthand notation for writing both very large and very small

numbers

Do you know this number, 300,000,000 m/sec? It is the speed of light.

Example: The Mass of the Sun The Sun has a Mass of 1.988 × 1030 kg. It would be too hard for scientists to write

1,988,000,000,000,000,000,000,000,000,000 kg (And very easy to make a mistake counting the zeros!)

Example: A Light Year (the distance light travels in one year)

It is easier to use 9.461 × 1015 meters, rather than 9,461,000,000,000,000 meters

Usagefor very large numbers

From scientific notation to standard form

From standard to scientific notation

The number 123,000,000,000 in scientific notation is written as

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

From standard to scientific notation

In the number 123,000,000,000 The coefficient will be 1.23 To find the exponent count the number of places from the decimal to the end of the number. In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:

To write a number in scientific notation:Put the decimal after the first digit and drop the zeroes.

Negative Exponents4

3

2

1

0

11

22

33

44

10 10 10 10 10 10000

10 10 10 10 1000

10 10 10 100

10 10

10 1

1 110 0.1

10 101 1

10 0.0110 1001 1

10 0.00110 10001 1

10 0.000110 10000

Meaning of Negative Exponents(Base 10)

110

10n

n

Meaning of Negative Exponents(any base)

1nn

aa

Negative Powers of 10Negative? What could be the opposite of multiplying? Dividing! A negative power means how many times to divide by the number. Negatives just go the other way!

Example: 5 × 10-3 = 5 ÷ 10 ÷ 10 ÷ 10 = 0.005Just remember for negative powers of 10:For negative powers of 10, move the decimal point to the left.

33

1 1 55 10 5 5 0.005

10 1000 1000

The exponent to which the base 10 is raised says how many places to move the decimal point. Positive means

move it to the right (because it is a repeated multiplication by 10), negative means to the left (repeated division by

10).

Summary

Because it makes it easier when you are dealing with very big or very small numbers, which are common in Scientific and Engineering work.

Example: it is easier to write (and read)

1.3 × 10-9 than 0.0000000013

Why Use It?

It can also make calculations easier, as in this example:

Example: a tiny space inside a computer chip has been measured to be 0.00000256 m wide, 0.00000014 m long and 0.000275 m high.

What is its volume?

Why use it?

Let's first convert the three lengths into scientific notation:

width: 0.000 002 56 m = 2.56×10-6

length: 0.000 000 14 m = 1.4×10-7

height: 0.000 275 m = 2.75×10-4

Then multiply the digits together (ignoring the ×10s):

2.56 × 1.4 × 2.75 = 9.856 Last, multiply the ×10s:

10-6 × 10-7 × 10-4 = 10-17 (this was easy: I just added the exponents -6, -4 and -7 together) The result is 9.856×10-17 m3

http://www.bing.com/videos/search?q=powers+of+ten+video&docid=4627106574827571&mid=5BFEAE2AD320F6F7D9CE5BFEAE2AD320F6F7D9CE&view=detail&FORM=VIRE1

http://htwins.net/scale/index.html

Links

Is this number written in scientific notation?

If yes, say why you think so, if not, rewrite it in scientific notation.

http://www.mathsisfun.com/index-notation-powers.html

Quiz

524.32 10