Using Dimensional Analysis Objective Make unit conversions Dimensional

Using Dimensional Analysis Objective: Make unit conversions

Dimensional Analysisis a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique to convert factors. First- Let’s practice some common factors….

Fill in the Missing Numbers 12 inches 1 foot = _____ 1 meter = _____ 100 centimeters 1 pound = _______ ounces 16 1 minute = ______ seconds 60 1 hour = ____ minutes 60 1 day = _____ 86, 400 seconds 1 hour= ____3, 600__ seconds

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 1 yd ? in. ? ft 1 mi ? ft 1 lb ? oz 1 pt ? c 1 qt 1 gal 1 hr 1 min 1 m 1 km ? pt ? qt ? min ? s ? cm ? m

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.

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.

Examples that cancel:

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

Convert 8 yards to feet… Make a decision: What conversion factor will you use? Set up the problem: Multiply the measurement by the conversion factor. Hint! Use the one that will cancel out the units Solve the problem: Perform the multiplication you want to change 8 x 3 = 24 feet

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 ∙

You Try it! One bag of apples weighs 64 ounces. How many pounds does it weigh? Darren drank 2 liters of water. How many milliliters of water did he drink?

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. 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.