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

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

Scientific Notation•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

Scientific Notation•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.

•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•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.

•4.4 x 1030 lbs.•Place the decimal pt. after the first # and then count to the end.

Scientific Notation•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

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•832,000,000 =8.32 x 108

Change to Scientific Notation

•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.

Change to Scientific Notation

•0.000722•Place the decimal just after the first number.

•Then count the # of places.•000722 = 7.22 x 10-4

Change to Standard Notation

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

Change to Standard Notation

•4.53 x 105

•Move the decimal pt. 5 places to the right.

•453000 = 453,000

Scientific Notation•(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

Try this one•820,000,000

Place the point after the 1st #

Count to the end8.2 x 108

8.2

Try this one•(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

Try this one•(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