Chapter 5 Dimensional Analysis

Please do notes in your composition book. Remember 🤔 Do not write every word Do not write every letter of each word I will put the things that you don’t need to (do not) write down in green. Please do notes in your composition book. (Since this is in green, you don’t have to write it down.)

Dimensional Analysis – Metric System This is a review. It is read “1 kilometer = 1x103 meters” “1 millimeter = 1/103 meters   Second Liter Meter M K h Dk Gram d c m  n Mega Kilo hecto deka Base deci centi milli micro nano x106 x105 x104 x103 x102 x101 x100 1/x101 1/x102 1/x103 1/x104 1/105 1/106 1/107 1/108 1/109

So the conversion is It is a definition because it has an equal sign (it is an equivalent. Still use the format. Conversion Factor is a fraction. What you are coming from is on bottom and going to is on top Starting # X Going to = Coming from

So convert 2 g to mg Starting # X Going to = Going to Coming from 2 g x 1 mg = 2 x 10-3 mg = 0.002 mg 1 x 103g This is the technically “proper” way to do it but the way I taught you in class is equally correct and much faster.

Are the units getting bigger or smaller as you move down the chart? What if you need to convert something that is not in the metric system? Are the units getting bigger or smaller as you move down the chart? We will use stick figures so you can see that this works with anything. Please copy down the chart in your composition bk. Write a summary sentence as an answer. “The units are getting _____________. The units are getting SMALLER. Biped 1 = 4 =6 =8 =7 =11 Generic quadruped- if you want to call it a dog or cat or other 4 legged creature it is fine. bird frog snake lizard

Draw a circle above the oval How to draw these: The “biped” is the basic human stick figure. Quadruped: Bird: Draw an oval Draw another smaller oval up and to the right Connect the head with the body and put 4 legs on. You can put ears & tail if you want. Draw a ½ circle & top it with a straight line Draw an oval Draw a circle above the oval Draw a sideways triangle for beak Connect the head to the body Draw straight lines at the bottom for feet

Draw a sideways oval below the 1st oval Frog Snake Lizard Draw an oval Draw a sideways oval below the 1st oval Draw a small circle for the eyes Draw a line for the mouth and a line partially across the lower oval to create the legs. Draw a squiggly line. Put a sideways triangle in front for the head Draw a long sideways oval Draw a sideways triangle for the head Draw a squiggly line for the tail & 4 lines for the feet.

Convert 30 to Starting “number” is 30 The equivalent 1 = 8 Write the 2 possible fractions. and Circle the correct fraction (the one with the bird on the bottom) Explain why: The starting number is birds so that is what needs to be cancelled. Set up the problem: Cancel and do the math everything on top is x everything on bottom is ÷

The answer is 240 . IT MUST HAVE THE UNIT… If you don’t want to draw the figures, give them a name and identify which is which.

Let’s try another and you do the steps. Convert 45 to . (This should be in your composition book because they are notes.) What is the first step? Write down the 1) instructions and the 2) actual step. (For now, I would like you to write all of the words. When you are more familiar with this, I will tell you what you can use for an abbreviation.) Remember, if it is in green you don’t have to write it down. Never write all of all the steps (words or sentences), only what you need to remember.

The 1st step: Write down what you start with. Convert 45 to . (You can use words instead but define them somewhere. Ex: = dog, = bird). What’s the next step? Instructions and actual step. (Copy what’s not in green.)

= 6 Write down the equivalent. (from the chart you just copied.) What’s the next step? Complete instructions and actual step. This is intentionally NOT green.

Turn equivalent into the 2 possible fractions. Or What’s the next step. Complete instructions and actual step. 6 1 1 6

Circle the fraction that you will use. To yourself think about why Circle the fraction that you will use. To yourself think about why. (What are the starting units? They will go on the bottom.) 6 1 1 6 OR

Starting is 45 sooooooo (Hurry and write it down. ) so circle this one Starting is 45 sooooooo (Hurry and write it down.) so circle this one. What’s the next step? Give the instructions and write the whole step. 6 1

Set up the problem. 45 6 1 X =

Cancel the units. 45 6 1 X = What’s the next step?

Are we finished? If not what else do we need to do? Solve. (Do the math.) 45 6 1 X = 270 Are we finished? If not what else do we need to do? ADD THE UNITS. Please do that.

Now, try another one on your own. Using the chart from above convert 38 to Remember to: do it in your comp bk write out the instructions for each step. do each step

Answer: 7 1 1 7 OR 1 7 to Starting value: 38 Equivalent: 7 = 1 Possible Fractions: Circle the proper fraction and explain why it is right. Set up and solve 38 x 7 1 1 7 OR 1 7

Dimensional Analysis Homework. Solve the following problems. Write the instructions for each step and write all the steps. Watch significant figures! Convert 125 birds to dogs. Convert 88 snakes to lizards. Convert 12 frogs to snakes. Convert 0.436 lizards to snakes. Convert 60 dogs to humans Convert 0.5580 dogs to humans Convert 98 frogs to birds