Scientific Notation

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SCIENTIFIC NOTATION ... a way to express very small or very large numbers that is often used in "scientific" calculations where the analysis must be very precise.

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Scientific Notation is a way of writing a number as a multiplication problem where…. the first number is greater than one but less than ten and the second number is a power of 10.

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POWERS OF 10 Notice that the negative powers are decimals.

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To Change from Standard Form to Scientific Notation: (1) Place decimal point such that there is one non-zero digit to the left of the decimal point.   (2) Count number of decimal places the decimal has "moved" from the original number.  This will be the exponent of the 10.   (3) If the original number was less than 1, the exponent is negative; if the original number was greater than 1, the exponent is positive.

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4,750,000 Use 4.75 (moved 6 decimal places) answer:  4.75 X 106 Example: The original number was greater than 1 so the exponent is positive.

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0.000789 Use 7.89 (moved 4 decimal places) answer:  7.89 x 10-4 The original number was less than 1 so the exponent is negative. Example:

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Try these: 61,500 = 4 6.15 x 10 84,960,000 = 7 8.496 x 10 321 = 2 3.21 x 10

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Try these: 0.000527 = -4 5.27 x 10 0.0000004 = -7 4 x 10 REMEMBER, the first number must be 1 or more, but less than 10. That means the first number before the decimal point can be 1, 2, 3, 4, 5, 6, 7, 8, or 9.

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To Change from Scientific Notation to Standard Form: (1) Move decimal point to RIGHT for POSITIVE exponent of 10.   (2) Move decimal point to LEFT for NEGATIVE exponent of 10.

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Example: 5.024 x 103 answer:  5,024   (3 places to right) Positive exponent- move decimal to the right.

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1.015 x 10-8 answer:  0.00000001015 (8 places to left) Negative exponent- move decimal to the left. Example:

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Write in standard form… try these: 5 1.09 x 10 = 109,000 4 4.2273 x 10 = 42,273 -3 9.42 x 10 = 0.00942

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Now turn to the scientific notation page in your packet. Practice writing numbers in scientific notation and in standard form. If there’s time, there’s a link is a 9 minute video about powers of ten on the next slide. It’s pretty cool…

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http://video.google.com:80/videoplay?docid=8095482682672703968&pr=goog-sl Click on the link to play the movie: http://www.youtube.com/watch?v=yCfDRvDWid0&mode=related&search= There’s shorter version of this on YouTube featuring The Simpsons. I don’t know if it will play at school. You may want to search Simpsons Power of 10 to see it at home.