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**Unit 5: The Metric System**

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**The Metric System is used everywhere except Burma, Liberia, and U.S.A.**

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5.1 Basic Terms and Conversions within the Metric System

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**SI System and U.S. Customary System**

Most countries of the world use the Systéme international d’unités or SI system. The SI system is referred to as the metric system in the United States. Two systems of weights and measures exist side by side in the United States today, U.S customary system and the metric system.

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**Advantages to Using Metric**

The metric system is the worldwide accepted standard measurement system. There is only one unit of measurement for each physical quantity. The SI system is based on the number 10, allowing less need for fractions and complicated conversions.

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**Basic Terms a little more than a quart volume L liter about 2.2 pounds**

mass kg kilogram a little more than a yard length m meter Comparison to Customary Common Use Abbrev Metric Term

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**Metric Prefixes Prefix Symbol Meaning kilo k 1000 x base unit hecto h**

deka da 10 x base unit base unit deci d 1/10 of base unit centi c 1/100 of base unit milli m 1/1000 of base unit

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**Changing Units within the Metric System**

To change from a smaller unit to a larger unit move the decimal point in the original quantity one place to the left for each larger unit of measure until you obtain the desired unit of measure. To change from a larger unit to a smaller unit, move the decimal point in the original quantity one place to the right for each smaller unit of measurement until you obtain the desired unit of measure.

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**Changing Units within the Metric System**

Measurement Kilo-meter Hecto-meter Deka-meter Meter Deci-meter Centi-meter Milli-meter Symbol km hm dam m dm cm mm Number of Meters 1000 100 10 1 0.1 0.01 0.001

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**Example: Changing Units**

Convert 54.6 m to km. Convert 15 L to mL. Convert 0.89 kg to cg – Poll!

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**Example: Changing Units**

Convert 54.6 m to km. Convert 15 L to mL. Convert 0.89 kg to cg. Solutions: Meters is a smaller unit than km. Move the decimal 3 places to the left, km. Liter is a larger unit than milliliter. Move the decimal point 3 places to the right, 15,000 mL. Kilogram is a larger unit than centigram. Move the decimal point 5 places to the right 0.89 kg = 89,000 cg

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Example: Application A case of fruit juice contains twenty-four 0.75 liter bottles. How many 250 milliliter glasses can you fill using one case of juice?

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Many prefixes!

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5.2 Length, Area, and Volume

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**Length A centimeter is a little less than a half of an inch.**

The meter is used to measure things that we normally measure in yards and feet. Centimeters and millimeters are used to measure what we normally measure in inches. A centimeter is a little less than a half of an inch. A millimeter is about the thickness of a dime. Example: The length of a pair of scissors would be measured in centimeters.

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**Area Area (of any shape) is always expressed in square units. Example:**

The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park. Area of a rectangle= length width.

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**Volume 1 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL Volume in Liters**

When a figure has three dimensions; length, width and height, the volume can be found. The volume of an item can be considered the space occupied by the item. Volume can be expressed in terms of liters or cubic meters. 1 m = kL 1 dm = L 1 cm = mL Volume in Liters Volume in Cubic Units

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Volume When the volume of a liquid is measured, the abbreviation “cc” is often used instead of cm3 to represent cubic centimeters. Example: An asthma patient must mix 0.25 cc of a drug with 2 cc of saline to use in an aerosol machine. How many milliliters of the drug will be administered? What is the total volume of drug and saline solution in milliliters?

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**Volume continued Solution:**

Since 1 cc is equal in volume to 1 milliliter, there will be 0.25 milliliters of the bronchodilator. The total volume is or 2.25 cc, which is equal to 2.25 mL.

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**Example: Finding the volume**

A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters? (Use V = πr²h for the volume of a cylinder.) Solution:

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5.3 Mass and Temperature

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**Mass Mass is a measure of the amount of matter in an object.**

Although weight and mass are not the same, on Earth they are proportional to each other, so we can treat them as the same thing. Mass is a measure of the amount of matter in an object. Weight is the measure of gravitational pull on an object.

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**Metric System Example: A man has the mass of about 75 kg.**

The kilogram is the basic unit of mass in the metric system. One kilogram weighs a bit more than 2 pounds. Example: A man has the mass of about 75 kg. The gram is relatively small and used in place of the ounce. Example: A nickel has the mass of about 5 g.

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Metric System The milligram is used in the medical and scientific fields. The metric tonne (t) is used to express mass of heavy items. One metric tonne = 1000 kg.

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**Example: Choosing an Appropriate Unit**

Determine which metric unit you would use to best express the mass of the following. a) A spider c) A bicycle b) A nickel d) A box of cereal Solution: a) c) b) d)

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**Volume and Mass of Water**

Volume in Cubic Units 1 m = kL = t (1000 kg) 1 dm = L = kg 1 cm = mL = g Mass of Water Volume in Liters

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**Example: Capacity A fish tank is 1 m long, 60 cm high and 260 mm wide.**

Determine the number of liters that the tank holds. What is the mass of the water in kilograms?

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**Example: Capacity continued**

Solution: Since 1 m3 of water = 1 kL of water, 0.156 m3 = kL, or 156 liters of water Since 1L = 1 kg, 156 L = 156 kg of water.

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**Temperature Water boils 212ºF 100ºC Body temperature 98.6ºF 37ºC**

The term degrees Celsius (ºC) is used to measure temperature. Water boils 212ºF 100ºC Body temperature 98.6ºF 37ºC Mild spring day 68ºF 20ºC Water freezes 32ºF 0ºC Description ºF ºC Temperature

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**Example: Choose °F or °C**

The temperature of Chicago on a summer day is about 35 __. The temperature of a person with a fever is about __. The temperature of cookies baking in the oven is 175 __. Solution: a) b) c)

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Conversions To covert from Celsius to Fahrenheit use the following formula. To covert from Fahrenheit to Celsius use the following formula.

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**Example: Conversions The equivalent temperature is about ____°C.**

The air temperature on a warm summer day is about 85°F. What is the equivalent temperature on the Celsius thermometer? Solution: The equivalent temperature is about ____°C.

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Example: Conversions The temperature of a cold glass of milk is about 5°C . What is the equivalent temperature on the Fahrenheit thermometer? Solution: The equivalent temperature is about _____°F.

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5.4 Dimensional Analysis and Conversions to and from the Metric System

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Dimensional Analysis Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement. A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1. Examples of unit fractions:

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**U.S. Customary Units 1 pint = 2 cups 1 year = 365 days**

1 cup (liquid) = 8 fluid ounces 1 day = 24 hours 1 ton = 2000 pounds 1 hour = 60 minutes 1 pound = 16 ounces 1 minute = 60 seconds 1 mile = 5280 feet 1 gallon = 4 quarts 1 yard = 3 feet 1 quart = 2 pints 1 foot = 12 inches U.S. Customary Units

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**Example: Using Dimensional Analysis**

A recipe calls for 8 cups of blueberries. How many pints is this? Solution: Convert 75 miles per hour to kilometers per hour.

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**Conversion to and from the Metric System - Length**

U.S. to Metric 1 inch (in.) ≈ 2.54 centimeters (cm) 1 foot (ft) ≈ 30 centimeters (cm) 1 yard (yd) ≈ 0.9 meter (m) 1 mile (mi) ≈ 1.6 kilometers (km)

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**Conversion to and from the Metric System - Area**

U.S. to Metric 1 square inch (in.2) ≈ 6.5 square centimeters (cm2) 1 square foot (ft2) ≈ 0.09 square meter (m2) 1 square yard (yd2) ≈ 0.8 square meter (m2) 1 square mile (mi2) ≈ 2.6 square kilometers (km2) 1 acre ≈ 0.4 hectare (ha)

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**Conversion to and from the Metric System - Volume**

U.S. to Metric 1 teaspoon (tsp) ≈ 5 milliliters (ml) 1 tablespoon (tbsp) ≈ 15 milliliters (ml) 1 fluid ounce (fl oz) ≈ 30 milliliters (ml) 1 cup (c) ≈ 0.24 liter (l) 1 pint (pt) ≈ 0.47 liter (l)

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**Conversion to and from the Metric System - Volume**

U.S. to Metric 1 quart (qt) ≈ 0.95 liter (l) 1 gallon (gal) ≈ 3.8 liters (l) 1 cubic foot (ft3) ≈ 0.03 cubic meter (m3) 1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)

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**Conversion to and from the Metric System - Weight (Mass)**

WEIGHT OR MASS U.S. to Metric 1 ounce (oz) ≈ 28 grams (g) 1 pound (lb) ≈ 0.45 kilogram (kg) 1 ton (T) ≈ 0.9 tonne (t)

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**Example: Volume and Area**

A gas tank holds 22.6 gallons of gas. How many liters is this? Solution: The area of a box is in2. What is its area in square centimeters?

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**Example: Converting Speed**

A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour. Solution: Since 62 km equals _____ mi, 62 kph is equivalent to _____ mph.

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**Example: Weight (Mass) Conversion for Medication**

A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given? Solution: The dosage of the medication is mg.

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Next week… Unit 6: Geometry!

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