Scientific Notation

Scientific Notation How much hydrogen does the sun burn each second? 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

A short-hand way of writing large numbers without Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

Scientific Notation Scientific Notation is made up of 2 parts. 1st Part = a number between 1 and 9 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

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

Try this one 8.2 x 10-8 .000000082

Multiplying with Scientific Notation (2.5x102 )( 2.5x 103 ) Multiply the coefficients 2.5 x 2.5 = 6.25 Add the Exponents 102 + 103 = 105 Put it together 6.25 x105

Multiplying with Scientific Notation (2.3 X 102)(3.3 X 103) Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 102 + 103 = 105 7.59 X 105

Multiplying with Scientific Notation (4.6 X 104) X (5.5 X 103) = ? Answer 25.3 x 107 Correct answer = 2.53 x108 (3.1 X 103) X (4.2 X 105) = ? Answer= 13.02 x 108 Correct Answer= 1.302 x 109

Dividing with Scientific Notation (3.3 X 104)/ (2.3 X 102) Divide the Coefficients 3.3/ 2.3 = 1.434783 Subtract the Exponents 104 - 102 = 102 Put them together 1.43 X 102

Dividing with Scientific Notation (4.6 X 104) / (5.5 X 103) = ? Answer= 0.836x 101 Correct answer = 8.36 (3.1 X 103) / (4.2 X 105) = ? Answer = .738x 10 -2 Correct answer =7.38x10-3