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

3. 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

4. Scientific Notation How much longer will the sun burn? 6,000,000,000 years.

5. 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

6. 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.

7. 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 10 30 lbs. Place the decimal pt. after the first # and then count to the end.

8. Scientific Notation 600,000,000 metric tons 6.0 x 10 ? 6.0 x 10 8 metric tons 6,000,000,000 years 6.0 x 10 9 years

9. Change to Scientific Notation 1570 Place the decimal just after the first number. 1.570 Then count the # of places 1570 = 1.57 x 10 3

10. 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 10 8

11. Change to Scientific Notation 2450 = 2.45 x 10 3 765,000,000 = 7.65 x 10 8 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.

12. 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

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

14. Change to Standard Notation 4.53 x 10 5 Move the decimal pt. 5 places to the right. 453000 = 453,000

15. Scientific Notation (5 x 10 3 )(4 x 10 5 ) 5 x 4 = 20 10 3 x 10 5 = 10 8 20 x 10 8 Now convert to Scientific Notation 2.0 x 10 9

16. Try this one 820,000,000 Place the point after the 1st # Count to the end 8.2 x 10 8 8.2

17. Try this one (6 x 10 2 )(3 x 10 7 ) 6 x 3 = 18 10 2 x 10 7 = 10 9 18 x 10 9 Now convert to Scientific Notation 1.8 x 10 10

18. Try this one (5 x 10 3 ) 2 = (5 x 10 3 ) 5 x 5 = 25 10 3 x 10 3 = 10 6 25 x 10 6 = 2.5 x 10 7