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

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

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

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

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

Prefixes in front of bases tell how big the “base” measurement is. Examples: Mm means 1 000 000 meters or 1 x 10 6 m mm means 0.001 meter or 1 x 10 -3 m m means just a meter or 1 x 10 0 m

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

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 10 6 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 ]

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…. 10 6, 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.

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.

Another example of improper to proper form of SN: 0.0052 x 10 5 becomes 5.2 x 10 2. The decimal goes after the first digit. Making the coefficient 3 steps larger, means that the multiplier must get 3 steps smaller.

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 2 nd EE 5 becomes 5.2 E2, which means 5.2 x 10 2.

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 10 5 is….0052 2 nd 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.

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.

Converting a SN metric unit to another metric unit using SN: Converting 6.3 x 10 3 μ g 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 10 3 x 10 -9 and you get 6.3 x 10 -6. See next slide for another example.

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

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.

Working with cubic length units, like m 3 and cm 3 Everything is just like changing between any other unit except that you let each step count as 3 decimal places. Example: 5.2 m 3 to cm 3 will be 6 steps to the right or x 10 6, to become 5.2 x 10 6. 7.9 x 10 12 mm 3 to m 3 is 9 steps left or x 10 -9, which becomes 7.9 x 10 12 x 10 -9 or 7.9 x 10 3 m 3.

Working with squared length units, like m 2 and cm 2 Everything is just like changing between any other unit except that you let each step count as 2 decimal places. Example: 5.2 m 2 to cm 2 will be 4 steps to the right or x 10 4, to become 5.2 x 10 4. 7.9 x 10 12 mm 2 to m 2 is 6 steps left or x 10 -6, which becomes 7.9 x 10 12 x 10 -6 or 7.9 x 10 6 m 2.

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