AKA How to make math ratios easy! Dimensional analysis AKA How to make math ratios easy!

What is Dimensional Analysis? Dimensional analysis is by far the most useful math trick you’ll ever learn. Maybe you have learned some algebra, but will you use it? Probably not after the test is done. For a fraction of the effort needed to learn algebra, you can learn “dimensional analysis.” First, let’s get rid of the big words. We are just talking about converting one thing to another. This is real life – seriously useful stuff!

What is Dimensional Analysis? This trick is about real-life math and physics – measurable stuff, stuff you can count. Anything you measure will have a number with some sort of “unit of measure” attached. We could also call this unit of measure, a “dimension.” A unit could be seconds, miles, grams, degrees, meters per second, peas per pod, or pizza slices per person.

So how do I do this trick? Example 1 : How many seconds are in one day? (write this word question down in your notes) First, don’t panic! Just break the problem down into small steps… Step 1 Ask yourself, “What units of measure do I want to have in the answer and what units of measure have I been given? If you can rephrase what you want to know using the word “per”, that means divided by in math. So for this problem, the answer we want is in the units: sec ………………………………………………………….. sec day

So how do I do this trick? Example 1 : How many seconds are in one day? Step 2 Ask yourself, “what do I know about these units” What do you know about how seconds or days relate to other units of time? You know that there are 60 seconds in 1 minute. You also know that in 1 minute there are 60 seconds. These are two ways of saying the same thing. You know that there are 24 hours in a day, or that 1 day contains 24 hours. 60 sec 1 min 60 min 1 hr 1 day 24 hr 1 min 60 sec 1 hr 60 min 24 hr 1 day

So how do I do this trick? Example 1 : How many seconds are in one day? Step 3 Ask yourself, “Which factors will get me across the bridge?” For every unit on top, we need a matching unit on bottom, until we can arrive at the end of the bridge. 60 sec 1 min 60 min 1 hr 1 day 24 hr 1 min 60 sec 1 hr 60 min 24 hr 1 day All of these “conversion factors” are equivalent. All we need to do now is pick from the ones that will get us across the bridge to where we want to end up.

So how do I do this trick? Example 1 : How many seconds are in one day? Step 4 Draw your bridge with pillars and cancel out matching units on top and bottom 60 sec 60 min 24 hr sec 1 min 1 hr 1 day day All of these “conversion factors” are equivalent. All we need to do now is pick from the ones that will get us across the bridge to where we want to end up.

So how do I do this trick? Example 1 : How many seconds are in one day? Step 5 Multiply 60 sec 60 24 = 60x60x24 = 86,400 sec 1 1 1 day 1 x 1 x 1 1 day

Summarize steps: Step 1 Write units you want at the end Step 2 Write things you know about these units Step 3 Pick the equivalent factors to cross the bridge Step 4 Cross out top and bottom matches Step 5 Multiply

Example 2 How many inches are in the length of a football field? Step 1 Step 2 Step 3 Step 4 Step 5

Example 2 How many inches are in the length of a football field? Step 1 end with . . . . . . . . . . . . . . . . . . . . . . . . . . . . in field Step 2 Step 3 Step 4 Step 5

Example 2 How many inches are in the length of a football field? Step 1 end with in field Step 2 12 in 3 ft 100 yds 5360 ft 1.6 miles what do I know? 1 ft 1 yd 1 field 1 mile 1 km Step 3 Step 4 Step 5

Example 2 How many inches are in the length of a football field? Step 1 end with in field Step 2 12 in 3 ft 100 yds 5360 ft 1.6 miles what do I know? 1 ft 1 yd 1 field 1 mile 1 km Step 3 12 in 3 ft 100 yds pick equivalent factors to cross bridge 1 ft 1 yd 1 field Step 4 Step 5

Example 2 How many inches are in the length of a football field? Step 1 end with in field Step 2 12 in 3 ft 100 yds 1 ft 1 yd 1 field Step 3 12 in 3 ft 100 yds pick equivalent factors to cross bridge 1 ft 1 yd 1 field Step 4 12 in 3 ft 100 yds cross out matching units 1 ft 1 yd 1 field Step 5 12 x 3 x 100 = 3600 in multiply 1 x 1 x 1 1 field

Example 3 If I measure 38.5 grams, how many milligrams do I have? Step 1 Step 2 Step 3 Step 4 Step 5

Example 3 If I measure 38.5 grams, how many milligrams do I have? Step 1 end with . . . . . . . . . . . . . . . . . . . . . . . . . . . . mg Step 2 Step 3 Step 4 Step 5

Example 3 If I measure 38.5 grams, how many milligrams do I have? Step 1 end with mg Step 2 1000 mg 100 cg 1000 g what do I know? 1 g 1 g 1 kg Step 3 Step 4 Step 5

Example 3 If I measure 38.5 grams, how many milligrams do I have? Step 1 end with mg Step 2 1000 mg 100 cg 1000 g what do I know? 1 g 1 g 1 kg Step 3 1000 mg pick equivalent factors to cross bridge 1 g Step 4 Step 5

Example 3 If I measure 38.5 grams, how many milligrams do I have? Step 1 end with mg Step 2 1000 mg 100 cg 1000 g what do I know? 1 g 1 g 1 kg Step 3 38.5 g 1,000 mg pick equivalent factors to cross bridge 1 g Step 4 38.5 g 1,000 mg eliminate top and bottom matching units Step 5 38.5 x 1000 = 385,000 mg

Example 4 If my car has a max speed of 125 miles per hour, how fast can it travel in meters per second? (hint: there are 0.62 kilometers in 1 mile) Step 1 Step 2 Step 3 Step 4 Step 5

Example 4 Did you calculate 21.53 meters per second? If my car has a max speed of 125 miles per hour, how fast can it travel in meters per second? (hint: there are 0.62 kilometers in 1 mile) Did you calculate 21.53 meters per second?

Example 5 If there are 5 peas per pod, and I can pick 32 pods per minute, how many peas will I have in 2 hours? Step 1 Step 2 Step 3 Step 4 Step 5

Example 5 Did you calculate 19,200 peas? If there are 5 peas per pod, and I can pick 32 pods per minute, how many peas will I have in 2 hours? Did you calculate 19,200 peas?