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I. SCIENTIFIC NOTATION

I. SCIENTIFIC NOTATION. A METHOD OF DEALING WITH VERY LARGE AND VERY SMALL NUMBERS IN SCIENCE. Very large numbers!. BOOM!. How far?. 92 000 000 miles. Very small numbers!. How wide is an atom?. 0.000 000 000 1 metres wide!. A. Writing Numbers in Scientific Notation. 5.67 x 10 5

malcolm-tyson
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I. SCIENTIFIC NOTATION

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  1. I. SCIENTIFIC NOTATION A METHOD OF DEALING WITH VERY LARGE AND VERY SMALL NUMBERS IN SCIENCE

  2. Very large numbers! BOOM! How far? 92 000 000 miles

  3. Very small numbers! How wide is an atom? 0.000 000 000 1 metres wide!

  4. A. Writing Numbers in Scientific Notation 5.67 x 105 coefficientbaseexponent Made up of three parts: thecoefficient, the base andthe exponent.

  5. B. Scientific Notation Rules: 1. The coefficientmust be between 1 and 9.9999999999999999999999999999999 2. Thebase must be 10 3. The exponent shows how many places the decimal moved.  5.67 x 105 coefficientbaseexponent

  6. Examples of Scientific Notation 363,000,000,000 = 3.63x 1011 0.00035 = 3.5x 10-4

  7. C. Scientific Notation Exponents • Numbers larger than 1, the exponent is positive • Example: 8.38 x 105 = 838,000 • Numbers less than 1, the exponent is negative • Example: 5.03 x 10-3 = 0.00503

  8. D. Scientific Notation for Large Numbers The point moved 7 places Add the decimal point Between 1 and 10 Move the point to get a number between 1 and 10 . 92 000 000 .

  9. The point moved 10 places. Negative sign for small numbers. E. Scientific Notation for Small Numbers Move the point to get a number between 1 and 10 . 0.000 000 000 1

  10. Examples of Scientific Notation 363,000,000,000 = 3.63x 1011 0.00035 = 3.5x 10-4

  11. Practice – Convert to Scientific Notation • 700 m c. 0.0054 kg • 38 000 m d. 0.000 006 87 kg 5.4 x 10-3 kg 7 x 102 m 6.87 x 10-6 kg 3.8 x 104 m

  12. The point moves 7 places to the right Zeros after the point aren’t needed. F. Changing back large numbers 8.6 0000000 . =86 000 000 Hint: Add 7 zeros, although you probably won’t need them all.

  13. -6 so remember to move point left for small numbers. G.Changingback small numbers Hint: Add 6 zeros to the left of the number. 5.16 000000 . = 0.000 00516

  14. Practice – Convert back to a number • 1.26 x 104 kg c. 9.02 x 103 kg • 5.36 x 10-2 m d. 7.6 x 10-5 m 12600 kg 9020 kg 0.0536 m 0.000076 m

  15. H. Multiplying using Scientific Notation • To multiply numbers in scientific notation, multiply the coefficients then add the exponents • Move the decimal point so that the number is in scientific notation

  16. Examples: Multiplying in Scientific Notation

  17. I. Dividing using Scientific Notation • To divide numbers written in scientific notation: • dividethe coefficients then • subtractthe exponent in the denominator (bottom) from the exponent in the numerator (top) => “top – bottom” or “first – second” • Express the final answer in scientific notation

  18. Example: Dividing Numbers in Scientific Notation

  19. Hint for converting an answer to scientific notation LARS: Left Add, Right Subtract • If you have to move the decimal to the LEFT, Add to the exponent • 12.6 x 103 = 1.26 x 104 • If you have to move the decimal to the RIGHT,Subtract from the exponent • 0.902 x 104 = 9.02 x 103

  20. Practice – Multiplying and Dividing 1.2 x 10-1 1.2 x 1011 3 x 101 2 x 10-1

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