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SCIENTIFIC NOTATION

SCIENTIFIC NOTATION. A “Shorter” Way. Algebra Readiness Academy Karen Yoho. Powers of Ten. 10 1. 1,000,000. 100. 10 2. 100,000. 10 4. 1000. 10,000. 10 3. 10 5. 10. 10 6. 10 2. = 100. = 10 . 10. = 1000. 10 3.

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SCIENTIFIC NOTATION

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  1. SCIENTIFIC NOTATION A “Shorter” Way Algebra Readiness Academy Karen Yoho

  2. Powers of Ten 101 1,000,000 100 102 100,000 104 1000 10,000 103 105 10 106

  3. 102 = 100 = 10.10 = 1000 103 = 10.10.10 = 10,000 104 = 10.10.10.10 = 100,000 105 = 100,000,000 108

  4. 7.452 x 10 = 74.52 7.452 x 100 = 745.2 7.452 x 1000 = 7452 7.452 x 10,000 = 74,520 7.452 x 100,000 = 745,200

  5. 612.3121 x 103 = 612.3121 x 1000 = 612,312.1 612.3121 x 106 = 612.3121 x 1,000,000 = 612,312,100

  6. The mass of the Earth is 5,973,600, 000,000,000,000,000,000 kilograms Wow! This is long! There has to be a better way!

  7. Scientific notation is a shorthand method of writing numbers that have a large number of digits. B x 10n Bis a number between 1 and 10. n is an integer.

  8. Writing a Number in Scientific Notation • Starting from the left, put a decimal point • to the right of the first digit that is not 0. • Count the number of digits that are passed • as you move to the right from this decimal • point to where the decimal point is in the • original number. (3) Use this number as an exponent for 10. (4) Drop the 0’s at the end of the original number. • Put a multiplication symbol between the • decimal number and the power of 10.

  9. In Scientific Notation 5,973,600,000,000,000,000,000,000 is 5.9736 x 10 24

  10. Saturn is approximately 762,700,000 miles from Earth. Scientific Notation: x 10 miles 7.627 8

  11. Prefixes kilo 1,000 103 mega 1,000,000 106 giga 1,000,000,000 109 tera 1,000,000,000,000 1012

  12. Names for Numbers 1,000,000 106 1 million 1,000,000,000 109 1 billion 1,000,000,000,000 1012 1 trillion 1,000,000,000,000,000 1015 1 quadrillion 1,000,000,000,000,000,000 1018 1 quintillion 1,000,000,000,000,000,000,000 1021 1 sextillion

  13. Negative Powers of Ten 10-4 0.001 10-1 0.00001 10-6 0.000001 0.01 10-3 0.1 10-2 10-5 0.0001

  14. 6.24 x 10-2 = 0.0624 9.06 x 10-4 = 0.000906 3.18 x 10-1 = 0.318

  15. Writing a Number in Scientific Notation IF THE NUMBER IS LESS THAN 1 • Starting from the left, put a decimal point • to the right of the first digit that is not 0. • Count the number of digits that are passed • as you move to the left from this decimal • point to where the decimal point is in the • original number. • Use the negative of this number as an • exponent for 10. (4) Drop any 0’s at the end of the original number. • Put a multiplication symbol between the • decimal number and the power of 10.

  16. x 10-3 1.7 0.0017 = 0.000205 = 2.05 x 10-4 0.825 = 8.25 x 10-1

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