dimensional analysis power point

8/6/2019 Dimensional Analysis Power Point

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Dimensional Analysis


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So how do you convert? Some of you are still confused, so

here is what I am going to call the "Ratio Method". This

method is the easiest, and it will help you when you need to

figure out which formula to use later in the class.

The first thing that you will need is a list of the Constants of

Conversion.

The best way to be able to use them easily is to have them

set out in a list, you can follow this example if you want to:

1 in = 2.54 cm12 in = 1 ft5280 ft = 1 mi1 m = 3.28 ft

(and so on for as many as youcan think of... include metric if

you can't remember, things like"1 cm = 10 mm")


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Lets start with a few examples of how to do

dimensional analysis. You will see this onHSAP and EOC!


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1 meter

We need to get edging for the pond in the Zen Garden. Wemeasured it out, and found that we need 35 feet. So we send you to

Home Depot to get it for us. But when you get there, the really coollooking stuff is from England, and only measured in Metric!Thankfully, you have your agenda with you, and you need toconvert.... And here's how:

We have feet, and need meters. So we set up:

35 feet 1 meter

But 1 meter = 3.28 feet, so we can substitute:

3.28 feet

1 meter

35 feet 1 meter


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35 feet 1 meter

But how did I know where to put the

"3.28 feet"?

I need "feet" to cancel out! So feet should be

on the bottom of the fraction.

3.28 feet


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Now we cancel out the "feet". We are left

with just "meter" for the unit!

35 feet 1 meter3.28 feet

So the unit will be "meter". Now we look at the math. Here

is where it gets tricky. You will really do 2 steps on this, but

it can be boiled down to just one step.


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We have:

35 1 meters 3.28

So we do:

35 1 = 35

And then:35 3.28 = 10.67


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So we end up with:35 feet = 10.67 meters


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Lets try another one, to see how else things might turn out...

In the coffee shop, a hot chocolatewill take 1 cup of milk. The shop has

4 gallons of milk to use for hot

chocolate. How many cups can we

make?

So we should set up:

4 gallons 1 cup

1 cup

But we know that 1 gallon = 16 cups.


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1 cup 16 cup1 gallon

4 gallons 1 cup

1 cup 1 gallon

What do we want to go away?

Gallons.So we put "1 gallon" on the bottom:

But now we have 1 gallon = 1 cup?

Not true... so we have to adjust the cups....

4 gallons


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16 cup1 gallon

4 gallons16 cup1 gallon

Check the fraction... Does 16 cups = 1 gallon?

Yes! So we cancel the gallons... That leaves

just "cup" for the unit.

4 gallons

Now do the math!


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4 16 = 6464 1 = 64

So we get:4 gallons = 64 cups


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What the math boils down to is:

You will always have a 1 on the top or the bottom. Thenyou have a different number. Here's what to do:

Fraction is: 1 on top

# on bottomDivide!

Fraction is: # on top

1 on bottomMultiply!


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Practice Conversions!

1. 7 cm = ____mm

2. 146 mm = ____cm3. 15 ft = _______yds

4. 3 ft = ____in

5. 6 in = _____cm6. 3.6 km = ______mi


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Check Conversions!

1. 7 cm = ____mm

2. 146 mm = ____cm3. 15 ft = _______yds

4. 3 ft = ____in

5. 6 in = _____cm6. 3.6 km = ______mi

70

1.465

36

15.24

2.24


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But sometimes it isn't that easy.... What if you don't have the

exact conversion on your list? There's way too many foranyone to copy down the entire thing... So here's how to do

the ones that may take a few steps.

Say that we need to get from inches to miles.

We need to convert 190,080 inches into miles.

I don't know about you, but I don't know how many inchesare in a mile. But I do know some that I can take a step

with!

I do have:

12 in = 1 ft5280 ft = 1 mi


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So start with inches to feet:

I do have:

12 in = 1 ft5280 ft = 1 mi

190,080 in 1 ft1 ft

Substitute the inches:

190,080 in 1 ft12 in

(remember that "in" should go away, so "in" is on thebottom, and check to make sure the fraction is right:

does 12 in = 1 ft?)


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Now do the math:

I do have:

12 in = 1 ft5280 ft = 1 mi190,080 1 = 190,080190,080 12 = 15,840

Now we have 15,840 ft.Next, we go to miles:

15,840 ft 1 mi5,280 ft

(remember that "ft" should go away, so "ft" is on thebottom, and check to make sure the fraction is right:

does 1 mi = 5280 ft?)


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We need to convert 15,840 feet into miles.

Now do the math:

I do have:

12 in = 1 ft5280 ft = 1 mi15,840 1 = 15,84015,840 5,280 = 3

Now we have:

190,080 in = 3 mi

Done!


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Now You try...

1 in = 2.54 cm

10 mm = 1 cm3 ft = 1 yd

1 ft = 3.28 m

1) 2 yd = ____ cm

2) 8 m = ____ in

3) 180 mm = _____ in


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Now You

Check...

1 in = 2.54 cm

10 mm = 1 cm3 ft = 1 yd

1 ft = 3.28 m

1) 2 yd = ____ cm

2) 8 m = ____ in

3) 180 mm = _____ in

182.88

314.96

7.087


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Metric Conversions

1 km = 1000 m

1 m 100 cm

1 m = 1000 mm

1 cm = 10 mm

These are the prefixes

used in the metric

system. Whether you

talk about grams, liters,

or meters, they are thesame.

Example for grams:

1 g = 100 cg

Example for Liters:

1 L = 1000 mL

Example for grams:

1 kg = 1000 g


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US to Metric Conversions

1 oz = 28.35 g1 kg = 2.2 lbs

1 mi = 1.609 km

1 yd = .9144 m

(Some)


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1 in3 = 16.3871 cm3

1 ft3 = .0283 m3

1 cm3 = .061024 in3

1 m3 = 35.315 ft3

1 yd3 = .76455 m3

1 m3 = 1.30795 yd3

1 tb = 3 tsp

1 c = 16 tb

1 pt = 2 c

1 qt = 2 pt

1 gal = 4 qt

1 c = 8 oz

1 mL = .0338 oz1 L = .2642 gal

Volume Distance1 in = 2.54 cm1 m = 1.09361 yd

1 cm = .3937 in

1 mi = 1.6093 km

1 ft = .3048 m

1 km = .6214 mi

1 m = 3.28 ft

1 yd = .9144 m

1 ft = 12 in

1 yd = 3 ft

1 mi = 5280 ft1 mi = 1760 yds

Weight1 oz = 28.3495 g

1 lb = .4536 kg

1 g = .03527 oz

1 kg = 2.2046 lb

1 lb = 16 oz1 ton = 2000 lb

Metric1 m = 100 cm

1 cm = 10 mm

1 km = 1000 m1 m = 1000 mm


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