# Scientific Notation

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```					Today’s Objective •To be able to express a very large number or very small number in scientific notation.

• What does the sun weigh?
• 4,400,000,000,000,000,000,000,000,000,000 lbs.

Scientific Notation

• 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.

Scientific Notation

• Let’s look at these large Numbers
• 4,400,000,000,000,000,000,000,000,000,000 lbs.

Scientific Notation

• 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.

Scientific Notation

• Let’s change these large Numbers to Scientific Notation…..
• 4,400,000,000,000,000,000,000,000,000,000 lbs.

Scientific Notation
30 10

• 4.4 x lbs. • Place the decimal pt. after the first # and then count to the end.

• 600,000,000 metric tons ? • 6.0 x 10 8 metric tons • 6.0 x 10 • 6,000,000,000 years 9 years • 6.0 x 10

Scientific Notation

Change to Scientific Notation

•1570
•Place the decimal just after the first number. 1.570 •Then count the # of places 1570 = 1.57 x 103

Change to Scientific Notation

•832,000,000 •Place the decimal just after the first number. •Then count the # of places 8 •832,000,000 =8.32 x 10

Change to Scientific Notation

• 2450 = 2.45 x 8 • 765,000,000 = 7.65 x 10 -4 • 0.000722 = 7.22 x 10 Notice that if the decimal moves right the exponent is negative and if it moves left, the decimal is positive.

3 10

Change to Scientific Notation

•0.000722 •Place the decimal just after the first number. •Then count the # of places. -4 •000722 = 7.22 x 10

Change to Standard Notation

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

Change to Standard Notation

•4.53 x •Move the decimal pt. 5 places to the right. •453000 = 453,000
5 10

Scientific Notation 3)(4 x 105) •(5 x 10 •5 x 4 = 20 3 x 105 = 108 •10 8 Now convert to •20 x 10 Scientific Notation 9 2.0 x 10

•820,000,000 8.2 Place the point after the 1st #

Try this one

Count to the end

8.2 x

8 10

Try this one 2)(3 x 107) •(6 x 10 •6 x 3 = 18 2 x 107 = 109 •10 9 Now convert to •18 x 10 Scientific Notation 10 1.8 x 10

•(5 x = 3) (5 x 103) •(5 x 10 •5 x 5 = 25 3 x 103 = 106 •10

3)2 10

Try this one

•25 x

6= 10

2.5 x

7 10

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