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Checklist of Metric System and Scientific Notation

Checklist of Metric System and Scientific Notation. Feel free to make good use the metric stair-step that you received. The 4 main base units that we use for mass, time, volume, and length are…. Gram (g) Second(s) Liter (L) Meter (m).

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Checklist of Metric System and Scientific Notation

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  1. Checklist of Metric System and Scientific Notation Feel free to make good use the metric stair-step that you received.

  2. The 4 main base units that we use for mass, time, volume, and length are… • Gram (g) • Second(s) • Liter (L) • Meter (m)

  3. Which two of those bases are not SI (International) units? • Liter – [volume is recognized as m3] • Gram – [international unit is kg since a gram is so small]

  4. From trillion to billionth, there are a variety of prefixes for different numerical meanings. • T • G • M • K • h • da • d • c • m •  • n

  5. Prefixes in front of bases tell how big the “base” measurement is. • Examples: • Mm means 1 000 000 meters or 1 x 106 m • mm means 0.001 meter or 1 x 10-3 m • m means just a meter or 1 x 100 m

  6. You can change from one unit to a different sized unit. • Using your stairstep, follow these examples: • A) 5.8 kg changed to mg is 6 steps to the right and thus becomes 5 800 000mg • B) 2500 cg changed to hg is 4 steps to the left, which becomes 0.25 hg

  7. Converting units using Scientific Notation (SN) • This time, we’ll do the same problem as in the previous slide, but do it in SN: • A) 5.8 kg changed to mg is 6 steps to the right and thus becomes 5.8 x 106 mg • B) 2500 cg changed to hg is 4 steps to the left, which becomes 2500 x 10-4 hg [Note: If you make this proper SN, it should be 2.5 x 10-1]

  8. What we did in the previous slide: • If moving “down” or to the right in the stair-step, then the multiplier, (the x10 part), has a POSITIVE exponent on the 10…. 106, in this case. • If moving “up” or to the left in the stair-step, then the multiplier has a NEGATIVE exponent on the 10…. 10-4, in this case.

  9. Changing an improper SN# to a proper one: • 2500 x 10-4 should be 2.5 x 10-1. Why? In proper form, the “coefficient” (2500) must have the decimal located after the first digit. • Because the 2500 got its decimal place moved to make the number 3 places smaller, then the “multiplier” must be made 3 times bigger. • 10-1 is 3 decimal places larger than 10-3.

  10. Another example of improper to proper form of SN: • 0.0052 x 105 becomes 5.2 x 102. • The decimal goes after the first digit. • Making the coefficient 3 steps larger, means that the multiplier must get 3 steps smaller.

  11. Working in SN on your TI-83/84 • Press Mode at the top left of calculator. • Select SCI for scientific notation • Or… select NORMAL for non-SN numbers. • Quit • Now, if you enter anything into the calculator, it will be Scientific mode. • Entering 0.0052 2nd EE 5 becomes 5.2 E2, which means 5.2 x 102.

  12. How do I enter an SN number on the calculator? • In case you haven’t figured-it-out yet, what you do to enter 0.0052 x 105 is… • .0052 2nd EE 5 enter • And you get 5.2 E 2 The big E stands for “x 10” Never enter “x 10 ^” into your calculator. You’ll probably get the problem wrong if you do so.

  13. What if I want to take a SN # and change it to a regular number on my calculator? • Do this, under MODE, change calculator to NORMAL • With the SN number on your screen, press ENTER, and the regular number will appear on screen • 5.2 E5 will become 520000 • Try it for yourself and see.

  14. Converting a SN metric unit to another metric unit using SN: • Converting 6.3 x 103μg to kg is 9 steps to the left or x 10-9. • So, tack on the x 10-9 and add the exponents. • Like this… 6.3 x 103 x 10-9 and you get 6.3 x 10-6. • See next slide for another example.

  15. Here’s another example: • Converting 0.0075 x 1015ng to Tg is 21 steps to the left or x 10-21. • So, do this: 0.0075 x 1015 x 10-21 will give you 0.0075 x 10-6 • Putting this in proper SN, it becomes 7.5 x 10-3.

  16. The next slides on cubic and squared metric units are more complicated. • They will be a bonus for any Chem students that can master them.

  17. Working with cubic length units, like m3 and cm3 • Everything is just like changing between any other unit except that you let each step count as 3 decimal places. • Example: 5.2 m3 to cm3 will be 6 steps to the right or x 106, to become 5.2 x 106. • 7.9 x 1012 mm3 to m3 is 9 steps left or x 10-9, which becomes 7.9 x 1012 x 10-9 or 7.9 x 103 m3.

  18. Working with squared length units, like m2 and cm2 • Everything is just like changing between any other unit except that you let each step count as 2 decimal places. • Example: 5.2 m2to cm2will be 4 steps to the right or x 104, to become 5.2 x 104. • 7.9 x 1012mm2to m2is 6 steps left or x 10-6, which becomes 7.9 x 1012 x 10-6or 7.9 x 106 m2.

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