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# 8 5 Scientific Notation

## by taco40 on Sep 18, 2008

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## 8 5 Scientific NotationPresentation Transcript

• Warm Up
• Simplify.
• Warm Up
• Simplify.
• Scientific Notation Making the writing of REALLY BIG NUMBERS easier And really small ones, too.
• Approximate Distance to Betelgeuse
• 6,000,000,000,000,000
• miles away
• Approximate Distance to Proxima Centauri
• 4.3 light years
• 4.3 x 186, 000 m/s x 60s x 60 m x 24 hr x 365 days is approximately
• 135,604,800,000 miles
• Or
• 39,900,000,000,000 km
Graphic from http://heasarc.gsfc.nasa.gov/ docs/cosmic/nearest_star_info.html
• Approximate Distance to S irius A
• 4.3 light years
• 8.6 x 186, 000 m/s x 60s x 60 m x 24 hr x 365 days is approximately…
• 271,209,600,000 miles
Image from space.com Sirius is called the Dog Star
• Big Numbers to write with less zeros
• 271,209,600,000
• 135,604,800,000
• 39,900,000,000,000
• What should we use?
• 271,209,600,000
• Step one:
• How many places can we move the decimal to just inside the left most digit?
• 271,209,600,000
• Looks like eleven places.
• Now insert the new decimal place and eliminate the end zeros.
• 2.71209600000
• and eliminate the end zeros.
• 2.712096
• To make 2.712096 equal to 271,209,600,000 we use a power of 10.
• In this case, 10 11
• 2.712096 x 10 ?
• We can multiply 2.712096 x 100,000,000,000 to get back to our original number.
• 100,000,000,000 is 10 11
• 2.712096x10 11 is written in scientific notation.
• Rules for Scientific Notation
• The first number MUST be between 1 and 10
• The operation is multiplication
• The second number is a power of 10.
• Check this with the above rules:
• .9808 x 10 5
• Better: 9.808 x 10 4
• Change us!
• 135,604,800,000
• 39,900,000,000,000
• 271,209,600
• Click for the next slide’s answers
• Change us to these answers.
• 135,604,800,000 =
• 1.356048 x 10 11
• 39,900,000,000,000 =
• 3.99 x 10 13
• 271,209,600 =
• 2.712096 x 10 8
• Let’s review
• To change 34,000,000,000,000,000 to scientific notation.
• Count the places from the far right to the place just to the right of the left-most digit (3). That’s 16 places.
• That’s the power of ten. In this case, 10 16
• Get rid of the extra unneeded zeros and multiply by the chosen power of ten.
• 3.4 x 10 16
• Very Small Numbers
• Let’s try 0.000079 as a number in scientific notation.
• Recall that negative exponents show fractions.
• The above number as a fraction would be seventy-nine millionths.
• How many places do we need to move the decimal. 0.000079
• We’ll end up with 7.9
• (between 1 and 10).
• 7.9 x 10 -?
• 7.9 x 10 -5
• Write in scientific notation: 0.003011
• How far to move the decimal?
• What number will be between 1 and 10?
• Since the number is less than one, we’ll have a negative decimal.
• 3.011 x 10 -3
It's OK to have negative exponents in sci-notation!
• Try Some
• 0.00004588
• 0.000307
• 0.0027
• Convert to scientific notation.
• 0.00004588 = 4.588 x 10 -5
• 0.000307 = 3.07 x 10 -4
• 0.0027 = 2.7 x 10 -3
• How do I combine numbers in scientific notation?
• (8.2 x 10 6 )(3.1 x 10 6 )
• 8.2 x 3.1 = 25.42
• 10 6 x 10 6 = 10 12
• 25.42 x 10 12 needs adjustment.
• (The 25.42 is NOT between 1 and 10)
• 2.542 x 10 13
• Try One.
• (1.9 x 10 8 )(2 x 10 10 )
• 1.9 x 2 = 3.8