Dimensional Analysis

What is Dimensional Analysis? Have you ever used a map? Since the map is a small-scale representation of a large area, there is a scale that you can use to convert from small-scale units to large-scale units—for example, going from inches to miles or from cm to km.

What is Dimensional Analysis? Ex: 3 cm = 50 km

What is Dimensional Analysis? Have you ever been to a foreign country? One of the most important things to do when visiting another country is to exchange currency. For example, one United States dollar equals 1509.7 Lebanese Pounds. (9/29/17)

What is Dimensional Analysis? Whenever you use a map or exchange currency, you are utilizing the scientific method of dimensional analysis.

What is Dimensional Analysis? Dimensional analysis is a problem-solving method that uses fractions to cancel units. It is used to go from one unit to another.

How Does Dimensional Analysis Work? A conversion factor, or a fraction that is equal to one (numerator equals the denominator), is used, along with what you’re given, to determine what the new unit will be.

Using the Conversion Factor Objective: Make unit conversions

Fill in the Missing Numbers 12 1 foot = _____ inches 1 meter = _____ centimeters 1 pound = _______ ounces 1 minute = ______ seconds 1 hour = ________ minutes 1 day = __________ seconds 100 16 60 60 What is the purpose of knowing these facts? Give me some examples. 86,400

Unit conversion factor A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these. 1 ft ? in. 1 yd ? ft 1 mi 1lb ? oz 1 pt ? c 1 qt ? pt 1 gal ? qt 1 hr ? min 1 min ? s 1m ? cm 1km ? m Fill in the blanks for as many as you know. Compare with your neighbor.

Unit conversion factor A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these. Ask for some reciprocals so you know they understand.

Choose a unit conversion factor that… Introduces the unit you want in the answer Cancels out the original unit so that the one you want is all that is left.

“Canceling” out Words

Practice: Choose the appropriate conversion factor. Inches to feet Minutes to hours Meters to centimeters

Let’s try some examples together… Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas? Given: 7 pizzas Want: # of slices Conversion: 12 slices = one pizza

Solution Check your work… 84 slices 7 pizzas 1 12 slices 1 pizza X =

Let’s try some examples together… 2. How old are you in days? Given: 17 years Want: # of days Conversion: 365 days = one year

Solution Check your work… 6205 days 17 years 1 365 days 1 year X =

Let’s try some examples together… 3. There are 2.54 cm in one inch. How many inches are in 17.3 cm? Given: 17.3 cm Want: # of inches Conversion: 2.54 cm = one inch

Be careful!!! The fraction bar means divide. Solution Check your work… 6.81 inches 17.3 cm 1 1 inch 2.54 cm X = Be careful!!! The fraction bar means divide.

A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units. What are the two conversion factors comparing quarts and gallons? Which one will “cancel” quarts? 16 qt 

Now, you try… Determine the number of eggs in 23 dozen eggs. If one package of gum has 10 pieces, how many pieces are in 0.023 packages of gum?

Multiple-Step Problems Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions. Example: How old are you in hours? Given: 17 years Want: # of hours Conversion #1: 365 days = one year Conversion #2: 24 hours = one day

Solution Check your work… 17 years 1 365 days 1 year 24 hours 1 day X = 148,920 hours

Assignment You must show your work in this dimensional analysis mini-unit. Write out the fractions so I know you understand the process not just the math.

Dimensional Analysis, part 2

Making Rate Conversions Use a unit conversion to convert the units within each rate

Convert 80 miles per hour to feet per hour. Convert 63,360 feet per hour to miles per hour.

You Try it! Convert 32 feet per second to inches per second. in A craft store charges $1.75 per foot for lace. How much per yard is this?

Word Problems The average American eats 23 pounds of pizza per year. Find the number of ounces the average American eats per year. The average American eats 368 ounces of pizza per year.

How many seconds in an hour? Word Problems… A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? Hint: Set up the words first. How many seconds in an hour? Once you’ve determined how many seconds in an hour, decide which conversion factor you should use. The car traveled 44 feet per second.