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Today’s Objective

Today’s Objective. GPS M7N1 . Students will be able to express a very large number or very small number in both scientific notation and standard form. Scientific Notation. What does the sun weigh? 4,400,000,000,000,000,000,000,000,000,000 lbs.

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Today’s Objective

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  1. Today’s Objective GPS M7N1. Students will be able to express a very large number or very small number in both scientific notation and standard form.

  2. 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

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

  4. 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

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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

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

  11. Change to Standard Notation • 4.53 x 105 • Move the decimal pt. 5 places to the right. • 453000 = 453,000

  12. 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

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

  14. 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

  15. 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

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

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

  18. Step 1 • Move decimal left • Leave only one number in front of decimal 93,000,000 = 9.3000000

  19. Step 2 • Write number without zeros 93,000,000 = 9.3

  20. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  21. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

  22. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

  23. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problems Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

  24. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 • 7.34 x 108 2) 8.7 x 1011

  25. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

  26. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

  27. 6.27 x 106 9.01 x 104 6,270,000 90,100 Write in Standard Form Move the decimal to the right.

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