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Practical Estimation Using Scientific Notation

Learn how to quickly estimate answers, convert numbers to scientific notation, and solve problems with power of ten calculations.

josephwwilliams
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Practical Estimation Using Scientific Notation

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  1. Practical EstimationUsingScientific Notation

  2. CreatedbyDick Heckathorn

  3. Can you quickly approximate an answer to the following problem? How many seconds are there in one year?

  4. Can you quickly determine which is larger? 3684 x 27.36 x 416.3 ? or 63.72 x 273 x 4175 ?

  5. Can you quickly approximate an answer to the following problem?

  6. A review of place holders

  7. 57,246.9318 5 ten-thousands 9 tenths 7 thousands 3 hundredths 2 hundreds 1 thousandths 4 tens 8 ten-thousandths 6 ones

  8. A review of what happens to a number when it is multiplied by ten (10).

  9. 2 2 x 10 = 20 2 x 10 x10 = 200 2 x 10 x 10 x 10 = 2000 2 / 10 = 0.2 2 / 10 / 10 = 0.02 2 / 10 / 10 / 10 = 0.002

  10. A review of numbers that are different by a power of 10.

  11. Number How number is formed 1 = 1 10 = 1 x 10 100 = 1 x 10 x 10 1000 = 1 x 10 x 10 x 10 10000 = 1 x 10 x 10 x 10 x 10 100000 = 1 x 10 x 10 x 10 x 10 x 10 1000000 = 1 x 10 x 10 x 10 x 10 x 10 x 10

  12. A review of how numbers are changed to power of ten format.

  13. Power Number How number is formed of 10 1 1 x no tens 100 10 1 x 10 101 100 1 x 10 x 10 102 1,000 1 x 10 x 10 x 10 103 10,000 1 x 10 x 10 x 10 x 10 104 100,000 1 x 10 x 10 x 10 x 10 x 10 105 1,000,000 1 x 10 x 10 x 10 x 10 x 10 x 10 106

  14. A review of how numbers are changed to power of ten format.

  15. Power of 10 Number How number is formed 100 1 1 10-1 0.1 1 / 10 10-2 0.01 1 / 10 / 10 10-3 0.001 1 / 10 / 10 / 10 10-4 0.0001 1 / 10 / 10 / 10 / 10 10-5 0.00001 1 / 10 / 10 / 10 / 10 / 10 10-6 0.000001 1 / 10 / 10 / 10 / 10 / 10 x 10

  16. Scientific Notation Is a system in which the numbers are expressed as the product of the COEFFICIENT which is a number that is equal to or greater than one but less than ten and the appropriate POWER OF TEN

  17. Here is an example.

  18. The Number 63847

  19. 63847 Same number in scientific notation 6.3847 x 104 Coefficient Power of Ten

  20. Let us now examine the steps to change a number to scientific notation format.

  21. Number to be Changed 76348

  22. 76348 First move the decimal point so that one non-zero digit is to the left of the decimal point. 7.6348

  23. Next determine what you did with the decimal point.

  24. 76348 7.6348 It was moved 4 places to the left.

  25. How does this number compare to the original number?

  26. 76348 7.6348 The number is 10,000 (104) times smaller.

  27. 76348 7.6348 To make the number in scientific notation the same as the original number, what must we do to the powers of ten?

  28. 76348 7.6348 We must multiply the number by ten to the fourth power (4). 7.6348 x 104

  29. Number to be Changed 0.000385

  30. 0.0003857 First move the decimal point so that one non-zero digit is to the left of the decimal point. 3.857

  31. Next determine what you did with the decimal point.

  32. 0.0003857 3.857 It was moved 4 places to the right.

  33. How does this number compare to the original number?

  34. 0.0003857 3.857 The number is 10,000 (104) times larger.

  35. 0.0003857 3.857 To make the number in scientific notation the same as the original number, what must we do to the powers of ten?

  36. 0.0003857 3.857 We thus multiply 7.6348 by 10 to the minus four power (10-4). 3.857 x 10-4

  37. Change the following number to scientific notation format. 724000 Check your answer on the next slide when finished.

  38. 724000 The answer is 7.24 x 104

  39. Change the following number to scientific notation format. 0.0000517 Check your answer on the next slide when finished.

  40. 0.0000517 The answer is 5.17 x 10-5

  41. Let us now solve a problem where the numbers are written in scientific notation.

  42. The Problem (3.1 x 102) x (2.0 x 104)

  43. (3.1 x 102) x (2.0 x 104) First separate the coefficients & powers of ten. (3.1 x 2.0) x (102 x 104)

  44. (3.1 x 102) x (2.0 x 104) (3.1 x 2.0) x (102 x 104) Next show how the powers of ten are combined. (3.1 x 2.0) x 10(2 + 4)

  45. (3.1 x 102) x (2.0 x 104) (3.1 x 2.0) x (102 x 104) (3.1 x 2.0) x 10(2 + 4) Finally finish the calculation. 6.2 x 106

  46. Let us solve another problem where the numbers are written in scientific notation.

  47. The Problem

  48. First separate the coefficients & powers of ten.

  49. Next show how the powers of ten are combined.

  50. Finally finish the calculation.

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