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Scientific Notation

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- What does the sun weigh?
- 4,400,000,000,000,000,000,000,000,000,000 lbs.
- How much hydrogen does the sun burn each second?
- 600,000,000 metric tons

- How much longer will the sun burn?
- 6,000,000,000 years.

- Let’s look at these large Numbers
- 4,400,000,000,000,000,000,000,000,000,000 lbs.
- 600,000,000 metric tons
- 6,000,000,000 years
- Each of these numbers can be written in a different form called Scientific Notation

- Scientific Notation is made up of 2 parts.
- 1st Part = a number between 1 and 10
- 2nd Part = x 10 to some power
- If it doesn’t have both parts, it is NOT Scientific Notation.

- Let’s change these large Numbers to Scientific Notation…..
- 4,400,000,000,000,000,000,000,000,000,000 lbs.
- 4.4 x 1030 lbs.
- Place the decimal pt. after the first # and then count to the end.

- 600,000,000 metric tons
- 6.0 x 10?
- 6.0 x 108 metric tons
- 6,000,000,000 years
- 6.0 x 109 years

- 1570
- Place the decimal just after the first number. 1.570
- Then count the # of places 1570

= 1.57 x 103

- 832,000,000
- Place the decimal just after the first number.
- Then count the # of places
- 832,000,000

=8.32 x 108

- 2450 = 2.45 x 103
- 765,000,000 = 7.65 x 108
- 0.000722 = 7.22 x 10-4

Notice that if the decimal moves right the exponent is negative and if it moves left, the decimal is positive.

- 0.000722
- Place the decimal just after the first number.
- Then count the # of places.
- 000722

= 7.22 x 10-4

- Now let’s go backwards and change from Scientific Notation to Standard Notation.

- 4.53 x 105
- Move the decimal point 5 places to the right.
- 453000

= 453,000

- (5 x 103)(4 x 105)
- 5 x 4 = 20
- 103 x 105 = 108
- 20 x 108

Now convert to Scientific Notation

2.0 x 109

- 820,000,000

8.2

Place the point after the 1st #

Count to the end

8.2 x 108

- (6 x 102)(3 x 107)
- 6 x 3 = 18
- 102 x 107 = 109
- 18 x 109

Now convert to Scientific Notation

1.8 x 1010

- (5 x 103)2 =
- (5 x 103) (5 x 103)
- 5 x 5 = 25
- 103 x 103 = 106
- 25 x 106 =

2.5 x 107