2. Do Now 10.15.13

7. Today’s Objective Students will be able to express a very large number or very small number in both scientific notation and standard form.

8. 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

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

10. 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

11. Scientific Notation Scientific Notation is made up of 2 parts. 1st Part = a number greater than or equal to 1, but less than 10 2nd Part = x 10 to some power If it doesn’t have both parts, it is NOT Scientific Notation.

12. 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.

13. 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

14. 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.

15. 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

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

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

18. 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

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

20. 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

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

22. The Distance From the Sun to the Earth 93,000,000

23. Step 1 Move decimal left Leave only one number in front of decimal

24. Step 2 Write number without zeros

25. Step 3 Count how many places you moved decimal Make that your power of ten

26. The power of ten is 7 because the decimal moved 7 places.

27. 93,000,000 --- Standard Form 9.3 x 10 7 --- Scientific Notation

28. Practice Problems 1)98,500,000 = 9.85 x 10 ? 2)64,100,000,000 = 6.41 x 10 ? 3)279,000,000 = 2.79 x 10 ? 4)4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6

29. More Practice Problems 1)734,000,000 = ______ x 10 8 2)870,000,000,000 = ______x 10 11 3)90,000,000,000 = _____ x 10 10 On these, decide where the decimal will be moved. 1)7.34 x 10 8 2) 8.7 x 10 11 3) 9 x 10 10

30. Complete Practice Problems 1)50,000 2)7,200,000 3)802,000,000,000 Write in scientific notation. 1) 5 x 10 4 2) 7.2 x 10 6 3) 8.02 x 10 11

31. Scientific Notation to Standard Form Move the decimal to the right 3.4 x 10 5 in scientific notation 340,000 in standard form 3.40000 --- move the decimal

32. Write in Standard Form 6.27 x 10 6 9.01 x 10 4 6,270,000 90,100