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Standard Index Form

Standard Index Form. What is standard index form and why do we use it?. It’s a way of writing either very big numbers or very little numbers. Without standard form, imagine how long it would take to write down or even pronounce these numbers…. A billion…. 1,000,000,000. A trillion

benjamin-barber
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Standard Index Form

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  1. Standard Index Form

  2. What is standard index form and why do we use it? It’s a way of writing either very big numbers or very little numbers. Without standard form, imagine how long it would take to write down or even pronounce these numbers…

  3. A billion… 1,000,000,000

  4. A trillion (million billion) 1,000,000,000,000

  5. A Quadrillion (million trillion) 1,000,000,000,000,000

  6. A googol 10,000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000

  7. The mass of the earth… 6,000,000,000,000, 000,000,000,000 kg

  8. The distance to the centre Of the milky way 250,000,000,000,000,000km

  9. The mass of an electron… 0.000000000000000 0000000000009109 g

  10. The mass of a water molecule… 0.0000000000000 0000000002994 g

  11. With standard form the numbers look much simpler…

  12. A billion… 1,000,000,000 1 x 109

  13. A trillion (million billion) 1,000,000,000,000 1 x 1012

  14. A Quadrillion (million trillion) 1,000,000,000,000,000 1 x 1015

  15. A googol 10,000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000 1 x 10100

  16. The mass of the earth… 6,000,000,000,000, 000,000,000,000 kg 6 x 1024 kg

  17. The distance to the centre Of the milky way 250,000,000,000,000,000km 2.5 x 1017 km

  18. The mass of an electron… 0.000000000000000 0000000000009109 g 9.109 x 10-28 g

  19. The mass of a water molecule… 0.0000000000000 0000000002994 g 2.994 x 10-23 g

  20. Convert 9 x 105 to a normal number 9 x 105 How many places the decimal point moves. LEFT if – RIGHT if + 0 0 0 0 0 9

  21. Convert 2.35 x 106 to a normal number 2.35 x 106 0 0 0 0 2 3 5

  22. Convert 1.9827 x 102 to a normal number 1.9827 x 102 1 9 8 2 7

  23. Convert 4 x 10-3 to a normal number 4 x 10-3 0 0 4 0

  24. Convert 2.901 x 10-6 to a normal number 2.901 x 10-6 0 2 9 0 1 0 0 0 0 0

  25. Convert 70000 to standard form 7 0 0 0 0 7 x 10 4

  26. Convert 32800000 to standard form 3 2 8 0 0 0 0 0 3.28 x 10 7

  27. Convert 823.91 to standard form 8 2 3.9 1 2 8.2391 x 10

  28. Convert 0.000008 to standard form 0.0 0 0 0 0 8 8 x 10 -6

  29. Convert 0.002091 to standard form 0.0 0 2 0 9 1 -3 2.091 x 10

  30. Write these in standard form: 311.2 x 107 9 3.112 x 10 (+2) 0.008 x 104 1 8 x 10 (-3) 1291.3 x 10-2 1 1.2913 x 10 (+3)

  31. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 11. These numbers are NOT written in standard form. Write each as a standard form number.

  32. Put the following numbers in order of size, smallest to largest… 628 ; 9.91 x 101 ; 2 x 103 ; 0.00011 x 10-1 ; 103 1.1x103 6.28x102 2x103 9.91x101 1.03x102 LARGEST SMALLEST 628 2x103 0.00011x10-1 9.91x101 103

  33. Put the following numbers in order of size, smallest to largest… 7.2 x 10-4 ; 0.004 ; 21 x 10-5 ; 0.0042 x 101 ; 9.99 x 10-5 4.2x10-2 7.2x10-4 2.1x10-4 4x10-3 9.99x10-5 SMALLEST LARGEST 4 x 10-3 0.0042 x 101 9.99 x 10-5 21 x 10-5 7.2 x 10-4

  34. Work out the following, leaving your answer in standard form… (2 x 105) x (3 x 103) x 105 x 103 2 x 3 x 10 8 6

  35. Work out the following, leaving your answer in standard form… (5 x 107) x (9 x 104) x 107 x 104 5 x 9 x 10 11 45 x 10 12 4.5

  36. Work out the following, leaving your answer in standard form… (6 x 104) x (5 x 10-2) x 104 x 10-2 6 x 5 x 10 2 30 x 10 3 3

  37. Work out the following, leaving your answer in standard form… (3.5 x 10-2) x (4 x 10-6) x 10-2 x 10-6 3.5 x 4 x 10 -8 14 x 10 -7 1.4

  38. Work out the following, leaving your answer in standard form… (9 x 109) ÷ (3 x 104) x (109 ÷ 104) (9 ÷ 3) x 10 5 3

  39. Work out the following, leaving your answer in standard form… (4 x 103) ÷ (8 x 107) x (103 ÷ 107) (4 ÷ 8) x 10 -4 0.5 5 x 10 -5

  40. Work out the following, leaving your answer in standard form… (1 x 10-2) ÷ (4 x 10-6) x (10-3 ÷ 10-6) (1 ÷ 4) x 10 3 0.25 2.5 x 10 2

  41. Work out the following, leaving your answer in standard form… (3.5 x 104) + (1.23 x 103) 3 5 0 0 0 + 1 2 3 0 3 2 6 3 0 3.623 x 10 4

  42. Work out the following, leaving your answer in standard form… (1.56 x 10-3) + (3.11 x 10-2) 0 . 0 0 1 5 6 + 0 . 0 3 1 1 . 0 0 3 6 6 2 3.266 x 10 -2

  43. Work out the following, leaving your answer in standard form… (5.92 x 105) - (1.091 x 105) 1 1 8 1 5 9 2 0 0 0 - 1 0 9 1 0 0 8 4 9 2 0 0 4.829 x 10 5

  44. Work out the following, leaving your answer in standard form… (1.03 x 10-2) - (8.16 x 10-3) 2 1 0 1 0 0 . 0 1 0 3 - 0 . 0 0 8 1 6 . 0 1 4 0 2 0 2.14 x 10 -3

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