September 21, 2010

Review:

Today we marked Exercise B in our Unit Conversion Practice sheet. Unlike Exercise A, which mainly involved single-step procedures, Exercise B required two steps:

Step One: The transition first to the unit of measurement that equalled 10 to the power of 0 (or just 1). This would be either grams (g), meters (m), seconds (s), or liters (L). (I like to think of these as the “basic” measurements”.)
Step Two: The move from grams/meters/seconds/liters to the desired unit.

After we were finished with the worksheet, we moved on to a new lesson: scientific notation.

Scientific Notation

Scientific notation is an useful method of simplifying very big numbers or very small numbers. So when you get a number like "325,000,000,000,000,000,000", you can be saved the trouble of writing all those pesky zeros down by instead writing just "3.25 x 10²⁰".

Big Numbers

1. If it's a really big number, always move the decimal place up until only one digit is still to the left of that little dot.
example: 770000000 becomes 7.70000000
2. Next, count the number of places the decimal dot has moved (in the example above, it's 8). This number will be the little number to the top-right corner of the 10 (the exponent, in other words, geez).
example: 7.70000000 x 10⁸

Small Numbers

1. If it's a really small number, always move the decimal place down until only one digit is still to the right of that little dot. 
example 1: 0.00041 becomes 4.1
If there's only one non-zero number at the end, place the dot just to the left of it.
example 2: 0.0004 becomes 4.0
2. Next, count the number of places the decimal dot has moved and that number will, again, be your 10's exponent (in the example 1 above, it's -4...negative because you moved the decimal dot up to make the number bigger, and so to revert back to its original form, the exponent must be negative).
example: 4.1 x 10^-4

Scientific Notation on Your Calculator:

Really, really easy stuff. Say you get an equation like (2.2 x 10⁴)(9.7 x 10^-12)

1.      First, turn your calculator on (to do this, press the ON button…there you go).

2.      Next, input the first number (in this case, 2.2)

3.      Now here comes the magic. Press the EXP button on your calculator. Your screen should now say 2.2  00. (Yes, the spacing is deliberate).

4.      Now input the exponent (in this case, it’s 4). Your screen should now say 2.2  04.

5.      Press the = button to get 22000. Remember this number.

6.      Now do the same for the other one. Input 9.7, press EXP, and add -12. Press the = button. Your screen should say 9.7- 12.

7.      Multiply 9.7- 12 by 22000 to get 0.000000213, or 2.13 x 10⁷. Ta-da!

 Extras:

Scientific Notation Explained

^ Just in case that thorough and articulate explanation wasn't enough, here's a video for you.

Scientific Notation Quiz

...and a quiz (calculator optional).



Afterwards, we finished up with…

Even More Unitary Rates

This is quite similar to what we did in Exercises A and B. Except this time, instead of the “basic” measurements being 10 to the power of 0 (or 1), they could be to the power of 2, or 3.

For example, before today we would use 1m = 100cm for conversions. Now, we can use 1m² which doesn’t equal 100cm, but 10000cm² (think of it as 100cm x 100cm).

Likewise, 1m³ would mean 100cm x 100cm x 100cm, which is equal to 1000000 cm³ or just 10⁶ cm³.

Conversions can be done using the exact same procedures we used for previous questions. Just be wary of the exponents.

An example from our notes. Notice how 1 Gm² is equal to 10¹⁸m². Before, we worked with → 1 Gm is equal to 10⁹m.



Homework:

Review WS - Scientific Notation worksheet - all

Even more UNITARY RATES worksheet - front page only

Quiz on the 27th.