DIMENSIONAL ANALYSIS MRS. COOK. WHAT IS DIMENSIONAL ANALYSIS?  Have you ever used a map?  Since the map is a small-scale representation of a large area,

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Presentation transcript:

DIMENSIONAL ANALYSIS MRS. COOK

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 Czech Koruna (Crowns).

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 the idea that any number or expression can be multiplied by one without changing its value.  It is used to go from one unit to another.

Equalities are two measurements with different units that are equal to each other. EQUALITIES

Each equality can be used to form two conversion factors. A conversion factor is a ratio of two units that is equal to one. 1 in = 2.54 cm CONVERSION FACTORS

WHY ARE CONVERSION FACTORS USEFUL? Because they are equal to one, a measurement can be multiplied by a conversion factor without changing the value of the measurement. 3 m x 1 x 1 x1 x 1 x1 Is still 3 m !!

1hand = 4 in 1 m = 100 cm 1 in = 2.54 cm Horses are measures in “hands”. Mrs. Cook’s horse was 16 hands tall. How tall was he in meters? EXAMPLE

SOLUTION

CONVERT YOUR AGE INTO SECONDS.

EXAMPLE  Mrs. Ethridge-Conti has ordered balloons for the homecoming dance. If she wants there to be 1150 balloons at the dance, how many packages should she order?  1 package contains a dozen balloons.

SOLUTION

EXAMPLE  Mrs. Cook is baking cookies for her students. The recipe calls for 1 bag of chocolate chips for every 2 dozen cookies. How many bags of chocolate chips should she buy to make 2 cookies for each of her 148 students?

SOLUTIONS

What is the mass of an elephant in kilograms if it weighs 3456 lbs? 1 lb = g 1 kg = 1000 g EXAMPLE

SOLUTION

A carat diamond was discovered in Africa. It is believed to be one of the finest specimens ever found. What is the mass of this diamond in pounds?  1 Carat = 200 mg  1 kg = 2.20 lbs  1 kg = g  1 g = mg EXAMPLE

SOLUTION

If Jules Verne expressed the title of his famous book, Twenty Thousand Leagues Under The Sea in basic SI units, what would the book be called? 1 league = 3 mi 1 mi = 5280 ft 1 m = yd 1 ft = 12 in 1 in = 2.54 cm EXAMPLE

SOLUTION

DENSITY MRS. COOK

DENSITY  A substance’s mass divided by its volume, typically written in g/cm 3  Density is the amount of matter within a certain volume  If the object is purely solid, then density determines if objects float. Water’s density is 1.00 g/cm 3. Objects with a density greater than water will sink and those with density less than water float.  The density depends on the material of the object, not its size or weight.

DENSITY PRACTICE  You measured a piece of Aluminum and it was found to have a volume of 6.30 cm 3 and a mass g. What is the density?

SOLUTION

DENSITY PRACTICE

SOLUTION

DENSITY PRACTICE  The density of a substance is 7.8 g/cm 3. What volume does 39 grams of it take up?  The density of water is 1.00 g/mL. What mass does 30.0 mL of water have?

SOLUTION