## MATH - SCIENCE INTEGRATION

### Converting from one unit of measurement to another.

 Quick! Tell me how many seconds are in a year!
 Most of us can't do that off the top of our heads.  So let's see how we can do it mathematically.

### Rules for solving problems

 RULES FOR UNIT CONVERSIONS USING DIMENSIONAL ANALYSIS The best way to understand the rules for converting is to see them in action.  Let's start with an example problem and go through the rules as we solve the problem.
 You will want to have a pencil, a calculator, and a piece of paper ready to go.

» See also: CONVERSION CHART (Reference)

• How much gift wrap do you need?
 Example Problem: A roll of Christmas gift wrap contains 2.5 meters of paper. What is the length of the paper in yards?

 Step 1:   Write down the known values and the unknown values. Known : length of paper in meters: 2.5 meters        Unknown :   length of paper in yards Step 2:    Find the conversion factor that gives a ratio between meters and yards.   You can use the reference table (Conversion Chart) included with this lesson. Conversion factor     1 meter = 1.09 yards

 Step 3:   Write the conversion factor as a fraction with the unit you want to convert to on top and set the problem up as an equation. 2.5 meters x  1.09 yards  =                           1 meter 2.725 yards You can see that the unit meters will cancel.

 Let's look at a problem in which we are converting to a larger unit.

• Metric Mayhem
 Problem:   Convert 325 millimeters to meters. Step 1:   Write down the known values and the unknown values. Known :   length in mm = 325   Unknown : length in meters

 Step 2:    Find the conversion factor that gives a ratio between meters and millimeters.   You can use the reference table (Conversion Chart) included with this lesson. Conversion factor   (use reference) 1 meter = 1000 mm

 Step 3:   Write the conversion factor as a fraction with the unit you want to convert to on top and set the problem up as an equation. 325mm = 1 meter =                 1000 mm .325 meters The unit millimeters will cancel.
 So far, the conversions solved have only required one conversion factor.  Let's solve a problem with several conversion factors.

• Time Flies!

 Problem:   How many centuries are in 237,439 days?

 Step 1:   Write down the known values and the unknown values. Known : number of days = 237,439 days     Unknown : number of centuries

 Step 2:    Find the conversion factor that gives a ratio between days and centuries. You can use the reference table (Conversion Chart) included with this lesson. Conversion factor :  We do not have a conversion factor for centuries/days.  So we need to go from days to the nearest unit we know.    We know that there are 365 days in a year.  We know that there are 100 years in a century.

 Step 3:   Write the conversion factor as a fraction with the unit you want to convert to on top and set the problem up as an equation. Equation: 237,439 days x 1year      x  1 century   =                        365 days       100 years       237,439   =     36500                                    6.51 centuries The units days and years will cancel.

• You Can't Forget This!
 Conversion Factors and Dimensional Analysis are mathematical problems.  Here are a couple of things that you must remember:
 Always remember to put the unit that you want to convert to on top! All conversion factors must be labeled! (meter, liter, year, etc .) It's time to practice solving unit conversions using dimensional analysis. Try Basic Conversion Problems first to give you some practice.

### Practice conversions.

 Practice makes perfect! You would never play in a football game or take on a champion cross country runner without a lot of practice yourself.  You should approach math the same way.  Practice, practice, practice!

• Basic Conversion Problems
 PRACTICE PROBLEMS DIRECTIONS:  Solve the following problems using dimensional analysis.  Show all work and don't forget to label all conversion factors (m, L, s, etc.).  If you need the conversion chart for reference, click on the link below. 1.  Convert 2,378 feet into meters. 2.  How many seconds are in 768 days? 3.  A car has traveled 7.2 miles.  How many inches did the car travel? 4.  How many centuries have you been alive? 5.  If a truck has a mass of 23,456 kg, what is its mass in milligrams? 6.  How many centiliters are in 3.7 gallons? 7.  Write 2,465 milliseconds as seconds. 8.  How many milligrams are in a 22 ounce steak? 9.  How many hours are there in 6.5 centuries? 10.  Convert 34,823 centimeters into miles.

» See also: Rules for solving problems
» See also: CONVERSION CHART (Reference)

• Application Problems
 CAN YOU APPLY IT? DIRECTIONS: Look at the situation below and see if you can use your new conversion skills to solve the problems. PROBLEM #1:
 You have received an email from your cousin Madeline in France, who wants to make your family's famous Pistachio Ice Cream as a surprise for her parents anniversary party. Unfortunately, Madeline can not find her mother's recipe for the ice cream and wants you to email the recipe to her.  She also asks you to send it with metric measurements instead of American measurements. You need to do some converting!

» See also: CONVERSION CHART (Reference)

• Making Ice Cream
 The recipe below is in English American units.  Now get out your paper, pencil, calculator, and conversion chart and convert the measurements to metric.  Show your work using dimensional analysis and then rewrite the recipe using only metric measurements.  Remember that all fractions need to be changed to decimals since the metric system uses decimals. PISTACHIO ICE CREAM You will need the following items to pack the ice cream freezer: 16 lbs of ice (crushed or chipped) 4 lbs of rock salt Shell and blanch: 4 oz pistachio nuts Pound them in a mortar with: A few drops of rose water Add to them: 1/4 cup sugar 1/4 cup cream 1 teaspoon almond extract 1/4 teaspoon green vegetable coloring Stir these ingredients until the sugar is dissolved.   Heat, but do not boil: 1 cup cream Add and stir until dissolved: 3/4 cup sugar 1/8 teaspoon salt Chill these ingredients.  Add the pistachio mixture and: 2 cups whipping cream 1 cup cream Put mixture into the canister for the ice cream churn.  Pack ice and salt around the canister.  Allow the pack to stand about 3 minutes before you start churning.   While waiting for the ice cream to harden, prepare the chocolate syrup topping.   TOPPING: Melt in a double boiler: 2 oz unsweetened chocolate 1 tablespoon butter Stir and blend well, then add: 1/3 cup boiling water Stir well and add: 1 cup sugar 2 tablespoons corn syrup Let the sauce boil readily over direct heat for about 3 minutes.  Reduce heat and cook for about 2 minutes more without stirring.  Add just before serving: 1 teaspoon vanilla extract The ice cream should be ready in about 20 minutes.  ENJOY!

### CONVERSION CHART (Reference)

CONVERSION CHART

 BRITISH AMERICAN UNITS Length: Volume: 1mile (mi) = 1760 yards = 5280 feet Liquid: 1 yard (yd) = 3 feet 16 fluid ounces (fl oz) = 1 pint 1 foot (ft) = 12 inches 2 cups = 1 pint 1 inch (in) = 1/12 foot = .083 feet 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) Dry: 2 pints = 1 quart (qt) 8 quarts = 1 peck (pk) 4 pecks = 1 bushel (bu)
 Mass: 16 ounces (oz) = 1 pound (lb) 2000 pounds = 1 ton (t) Time: 60 seconds (s) = 1 minute 60 minutes = 1 hour (hr) 24 hours = 1 day 7 days = 1 week 365 days = 1 year (yr) 10 years = 1 decade 100 years = 1 century METRIC UNITS: Length: 1 kilometer (km) = 1000 meters (m) 1 hectometer (hm) = 100 meters 1 dekameter (dam) = 10 meters Base Unit for Length: 1 meter = 1m 1 decimeter (dm) = .10 meters (1m = 10 dm) 1 centimeter (cm) = .01 meters ( 1m = 100 cm) 1 millimeter (mm) = .001 meters (1m = 1000mm) Volume: 1 kiloliter (kL) = 1000 liters (L) 1 hectoliter (hL) = 100 liters 1 dekaliter (daL) = 10 liters Base Unit for Volume: 1 liter = 1L 1 deciliter (dL) = .10L (1 liter = 10 dL) 1 centiliter (cL) = .01L (1liter = 100cL) 1 milliliter (mL) = .001L (1liter = 1000mL) Mass: 1 kilogram (kg) = 1000grams (g) 1 hectogram (hg) = 100 grams 1 dekagram (dag) = 10 grams Base Unit for Mass: 1 gram = 1g 1 decigram (dg) = .10g (1g = 10dg) 1 centigram (cg) = .01cg (1g = 100cg) 1 milligram (mg) = .001mg (1g = 1000mg) 1 metric ton = 1000 kg
 CONVERSIONS BETWEEN METRIC AND AMERICAN SYSTEMS Length (Metric to American): Length (American to Metric): 1km = 0.6mi 1mi = 1.6km 1m = 39.37in 1yd = 0.9m 1cm = 0.4in 1ft = 30cm 1in = 2.5cm Volume (Metric to American): Volume (American to Metric): 1L = 1.06qt 1qt = .95L 1 gal = 3.8L Mass (Metric to American): Mass (American to Metric): 1kg = 2.2lb 1lb = 0.45kg 1g = 0.04oz 1oz = 28.4g