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 600,000,000 metric tons 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 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 4.4 x 1030 lbs. 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 =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 Now convert to Scientific Notation 2.0 x 109

8.2 x 108 Try this one Count to the end 820,000,000 8.2 Place the point after the 1st # Count to the end 8.2 x 108

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 2.5 x 107 (5 x 103)2 = (5 x 103) (5 x 103) 5 x 5 = 25