Dimensional Analysis - USING UNITS TO SOLVE A SPECIFIC PROBLEM Can mean that you don’t have to memorize equations for many problems!

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Presentation transcript:

Dimensional Analysis - USING UNITS TO SOLVE A SPECIFIC PROBLEM Can mean that you don’t have to memorize equations for many problems!

Dimensional Analysis Uses dimensions or units to solve problems General Math Rule: Do the same thing with the units that you do with the numbers Ex: 2 m x 3 m = ? ANS: 6 m 2 since 2 x 3 = 6 & m x m = m 2

Dimensional Analysis Ex 2: 30. g / 15. mL = ? ANS: 2.0 g/mL

Review: Multiplying Fractions What is A x 3 A = ? ANS: A’s cancel giving 3 as the answer

Review: Multiplying Fractions What is 2 ft x 12 in 1 ft = ? ANS: ft cancels giving 2x12/1 = 24 in as the answer

You can use DIMENSIONAL ANALYSIS to SOLVE PROBLEMS LEARN HOW TO DO THIS & YOU MAY NEVER HAVE TO MEMORIZE ANOTHER EQUATION!!!!

How to Apply Dimensional Analysis The following presentation demonstrates how to apply Dimensional Analysis

Read the problem Determine the GIVEN with its unit Determine UNKNOWN What unit are you seeking? Example: How many yards is 56 inches? ? ? ??? ? ? ??

Track Method Write the given with it’s unit in the first numerator of your R.R. track 56 inches

Place the same unit in the next fraction’s denominator where it will be ready to cancel later. 56 inches inches

What conversion factors do you know that will get you closer to the unit you want in the final answer? I have 56 inches I want yards HaveWant I Know (conversion factors) I know 12 in = 1 footand 3 feet = 1 yard

Pick a conversion factor that will get you closer to the unit you want in the final answer. This becomes the unit at the top of the new fraction. I know 12 inches = 1 foot 56 inches inches 12 1 foot

Is the unit on top the one you WANT to end up with? YES NO then do the math find another conversion factor that gets you closer

My “given” unit cancelled and I’m left with feet. I WANT yards I HAVE feet 56 inches inches12 1 foot I KNOW 3 feet = 1 yard so... 3 feet 1 yard

The last step is to check your cancelled units and do the math! 56 x 1 x 1 ÷ 12 ÷ 3 = 1.5 yards Congratulations! Now you can solve word problems by dimensional analysis! 56 inches inches12 1 foot 1 yard 3 feet

PRACTICE PROBLEMS: 1.How many minutes in a year? 2.The Baconater from Wendy’s has 8 strips of bacon. How many strips of bacon are there in 16 Baconaters? 3.It is 5954 m from KHS to Hwy 59. How many miles is that? Hint: There are 1.61 km in a mile & 1 km = 1000 m

Let’s Do The Lab!