Scientific Notation Notes You will need your own paper.
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Transcript of Scientific Notation Notes You will need your own paper.
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Scientific Notation Notes
You will need your own paper.
![Page 2: Scientific Notation Notes You will need your own paper.](https://reader035.fdocuments.in/reader035/viewer/2022072008/56649d745503460f94a5473f/html5/thumbnails/2.jpg)
Purpose:Often in science we work with numbers that are really small or really big. Not wanting to spend a lot of time writing zeros, we use scientific notation instead. Scientific notation works on powers of ten, making the zeros that we don’t want to write the exponents of ten.
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Examples: 1,000,000 = 1 x 106
10,000 = 1 x 104
100 = 1 x 102
10 = 1 x 101
0.1 = 1 x 10-1
0.01 = 1 x 10-2
0.0001 = 1 x 10-4
0.000001= 1 x 10-6
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Examples:A. 35,000 = 3 . 5 0 0 0. = 3.5 x 104
B. 0.0042 = 0 . 0 0 4 . 2 = 4.2 x 10-3
C. 0.0000815 = 0 .0 0 0 0 8 . 1 5 = 8.15 x 10-5
Note: the decimal gets moved behind the first nonzero digit - ALWAYS!
To take a number out of scientific notation just reverse the direction the decimal has moved
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Significant Digits and Scientific Notation
Keep the Sig Digs the same!
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In scientific notation it is the significand (the front part) that contains the significant digits. Again, nothing after the “x” sign counts towards signifcant digits.
5.423 x 109 has 4 sig digs9.0 x 10-4 has 2 sig digs1.0000008 x 102 has 8 sig digs
When converting into or out of scientific notation you MUST KEEP THE SIG DIGS THE SAME.
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Try These:Turn these into scientific notation:A) 405,000B) 0.00203C) 0.009000D) 40
Turn these into standard notation:E) 7.601 x 106
F) 4.20 x 10-3
G) 1.0000 x 102
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Try These:Turn these into scientific notation:A) 405,000 4.05 x 105
B) 0.00203 2.03 x 10-3
C) 0.009000 9.000 x 10-3
D) 40 4 x 101
Turn these into standard notation:E) 7.601 x 106 7601000F) 4.20 x 10-3 0.00420G) 1.0000 x 102 100.00
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Using Scientific Notation in a Calculator
It’s not like you think…
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You must communicate with the calculator in the way it was meant to communicate. This is most important with scientific notation.
For example: 6.022 x 1023 ÷ 2.52 x 1014 = ?
Instead of using “x 10^” the calculator needs the “EE” button. On the screen you would see:
6.022E23÷2.52E14, and it would equal 2.39E9, which you would write down as 2.39 x 109.
Without the “EE” button you’d get the answer 2.39 x 1037 - which is completely wrong.
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A Final Thought About Scientific Notation
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Lets say I counted 100 Skittles, and wanted to report this to a friend. He would think I rounded to the hundreds place, but I counted each skittle and know it to the ones place. How do I show this?
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Lets say I counted 100 Skittles, and wanted to report this to a friend. He would think I rounded to the hundreds place, but I counted each skittle and know it to the ones place. How do I show this?
Scientific Notation to the rescue!
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Lets say I counted 100 Skittles, and wanted to report this to a friend. He would think I rounded to the hundreds place, but I counted each skittle and know it to the ones place. How do I show this?
Because I want the ones place to be a significant digit it will report it as 1.00 x 102. Now both zeros are significant and my friend knows I rounded to the ones place.
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Try These:
Round 4,500,000 to four sig digs.
Round 0.002 to three sig digs.
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Try These:
Round 4,500,000 to four sig digs.4.500 x 106
Round 0.002 to three sig digs.
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Try These:
Round 4,500,000 to four sig digs.4.500 x 106
Round 0.002 to three sig digs.2.00 x 10-3