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SCIENTIFIC NOTATION: Abbreviating numbers

SCIENTIFIC NOTATION: Abbreviating numbers. 1. 2. 3. 4. 5. What is an EXPONENT?. A SUPER SCRIPT after “x 10” or “E” Ex: “x 10 5” or “ E 5” Denotes how many powers of ten 10 5 = 10 x 10 x 10 x 10 x 10 Answer is a 1 followed by zeros (defined by the exponent) . 100,000. 5.

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SCIENTIFIC NOTATION: Abbreviating numbers

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  1. SCIENTIFIC NOTATION:Abbreviating numbers

  2. 1 2 3 4 5 What is an EXPONENT? • A SUPERSCRIPT after “x 10” or “E” • Ex: “x 105” or “E5” • Denotes how many powers of ten • 105 = 10 x 10 x 10 x 10 x 10 • Answer is a 1 followed by zeros (defined by the exponent) 100,000 5

  3. BIG NUMBERS Positive Exponents 5,987,774,231,541

  4. Numbers smaller than 1 Negative Exponents 0.0000076319

  5. Moving the decimal (+) MOVE THE DECIMAL TO THE RIGHT 3 TIMES 5 34 x 10 . 5 34 0 . .

  6. -4 2 78 x 10 . Moving the Decimal (-) MOVE THE DECIMAL TO THE LEFT TIMES 0 0 0 0 2 78 . .

  7. PRACTICE: • 4.67 x 105 • 1.94 x 101 • 7.69 x 100 • 2.48 x 10-2 • 7.35 x 10-6 • 2.52 E -4 = 467000 = 19.4 = 7.69 = 0.0248 = 0.00000735 = 0.000252

  8. Converting to Scientific Notation • FIND THE DECIMAL • MOVE THE DECIMAL SO THE BASE NUMBERIS LESS THAN 10, GREATER THAN 1 • COUNT THE NUMBER OF JUMPS 6420 . . .

  9. Cont. 4. ROUND ANSWERS SO THEY HAVE THREE (3) DIGITS STARTING FROM THE LEFT 5. ADD “X 10” (or E) 6. THE NUMBER OF JUMPS IS YOUR EXPONENT! 3 642 0 x 10 . 1 2 3

  10. PRACTICE: • 56420 • 123 • 718134 • 6132 = 5.64 x 104 = 1.23 x 102 = 7.18 x 105 = 6.13 x 103

  11. NEGATIVE EXPONENTS 3 If your number is less than 1 you will have a negative exponent! - 000345 345 x 10 . . .

  12. PRACTICE: • 0.0184 • 0.000567 • 0.06 • 0.00057912347 = 1.84 x10-2 = 5.67 x10-4 = 6.00 x10-2 = 5.79 x10-4

  13. Three Number Rule • If there are not enough numbers add zeros • If there are too many numbers round

  14. Rounding 7 • START FROM THE LEFT AND COUNT THE FIRST 3 NUMBERS • IF THE FOURTH NUMBER IS A 5 OR ABOVE ROUND UP! • DROP UNNECESSARY NUMBERS 5 5 447 446 527 x 10 x 10 . 1 2 3

  15. PRACTICE: =2.38 x 104 =1.15 x 10-4 =4.69 x 105 =1.00 x 100 =2.10 x 106 =2.00 x 10-6 Put the problem in Sci. Not. 1st :Round • 23794 • 0.0001146 • 468992 • 0.9999 • 2100100 • 0.000002

  16. SCIENTIFIC NOTATION PRACTICE Convert the following to normal notation: • 5.23 x 103 • 2.90 x 10-9 • 4.18 x 10-5 • 2.71 E7 Convert the following to SCIENTIFIC notation (ROUND TO 3 DIGITS): • 0.00854 • 349001 • 0.03 • 1238 Round to 3 DIGITS (you have to put them in sci. not. first!) • 6349 • 0.3487 • 7956143278 • 0.0000000000000799

  17. Prefixes: • Super- • Above • Ex: X2 • Sub- • Below • Ex: X2

  18. Exponent Rule! • DECIMAL MOVES  • EXPONENT becomes MORE POSITIVE (+1) • DECIMAL MOVES  • EXPONENT becomes MORE NEGATIVE (-1) 0.214 x 10-2 2.14 x 10-2 2.14 x 10-3

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