Unit Analysis

Unit Analysis AKA

• Unit conversions• Dimensional Analysis

Unit Analysis Use conversion factors to solve math

problems When you divide a number by itself,

that fraction is equal to one A conversion factor is a fraction that

is equal to one. It is formed from a valid relationship between numbers with units.

Finding Conversion FactorsEx: 1 = 1 because 1=1 1

Ex: 4.5 = 1 because 4.5=4.5 4.5

So… if 1 ft = 12 in then1 ft = 1 or 12 in = 112 in 1 ft

If 60 sec. = 1 min then1 min = 1 or 60 sec = 160 sec 1 min

Multiplying a number by a conversion factor is the same as multiplying by 1, but it allows you to change units.

Unit Analysis Treat units like #s

• Units cancel like numbers: when the same unit is the numerator and denominator it cancels to one

Ex: meter = 1 meter

Ex: hours = 1 hours

It works with abbreviations too: mL = 1 mL

g = 1g

How many quarters are in $3. 75

Using Unit Analysis

1. Write the known quantity.2. Figure out the units you need to end

up with.3. Multiply by conversion factors to get

from the original units to the final.4. Like units cancel top & bottom.5. NO NAKED NUMBERS!

How many quarters are in $3. 75

Start with what you know:

What unit do we need to end with?

What conversion unit(s) do we need to use to solve this problem?

No naked numbers in work or answer!

Cancel the units and multiply the numbers:

3.75 dollars

quarters

4 quarters1 dollar

3.75 dollars

4 quarters1 dollar

= 15.0 quarters

DO NOW Take out notebook and homework leave on desk.

Attach objectives in notebook Try to use unit analysis to calculate • how many dollars you have if you have 177 nickels?

• How many inches are in 2.76 ft?

Look at Pink homework Take out homework for me to stamp

While waiting complete part 1 # 3 using unit analysis (it is ok- and encouraged- to work together as I will be stamping off homework unable to answer many specific questions)

If you have finished this either compare with a partner or help another student.

Example: How many seconds are in 30 days?

30 Days24 hr1 day

= Sec.60 min1 hr

60 sec1 min

2,592,000

What is the mass in grams of3.0 in3 of gold?

There are 2. 54 cm in 1.00 inch• Therefore we can use this as a conversion factor

There are 19.32 g of gold in 1.00 cm3 of gold• Therefore we can use this as a conversion factor

2.54 cm1.00 in

3.0in3 2.54cm 2.54cm 2.54cm 19.32g = 950 g 1.00 in 1.00 in 1.00 in 1.00 cm3

19.32 g1.00 cm3

Partner explanation problems

1. You are working in a factory and you have 15462 nails that you need to pack and ship. Each box can fit 150 nails and each crate can hold 15 boxes. How many crates will you fill with nails?

2. A runner ran 3680 m. If there are 1.09 yards in one meter and 120. yards in a football field, how many football fields is this?