Basic Terms and Conversions within the Metric System 5.1 Basic Terms and Conversions within the Metric System

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.

Advantages to Using the Metric System 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.

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

Metric Prefixes Prefix Symbol Meaning kilo k 1000 × base unit hecto h deka da 10 × 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

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.

Changing Units within the Metric System Measure of length kilometer hectometer dekameter Symbol km hm dam Number of meters 1000 m 100 m 10 m Measure of length meter decimeter centimeter millimeter Symbol m dm cm mm Number of meters 1 m 0.1 m 0.01 m 0.001 m

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, 0.0546 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

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? Solution: The case of juice contains 24(0.75) = 18 L. Converting 18 L = 18,000 mL. If each glass hold 250 mL, then glasses can be filled.

Test yourself How many dL are in 17.634 L? Type your answer now.

Test yourself again How many kg are in 8235 mg?

5.2 Length, Area, and Volume

Length 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.

Area Areas are 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. Solution: Area = length  width.

Area, an exception One common unit of area is a hectare, which is a hectometer square. This is the same as 10,000 square meters.

Volume 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 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL Volume in Liters Volume in Cubic Units

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 bronchodilator with 2 cc of saline to use in an aerosol machine. How many milliliters of the bronchodilator will be administered? What is the total volume of drug and saline solution in milliliters?

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 0.25 + 2 or 2.25 cc, which is equal to 2.25 mL.

Example: Volume Application A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters? Solution:

Area application A sheet of A4 (European) paper is 210 mm by 297 mm. What is the area a sheet of A4 paper in m2?

5.3 Mass and Temperature

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

Metric System The kilogram is the basic unit of mass in the metric system. 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. 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.

Example: Choosing an Appropriate Unit Determine which metric unit you would use to express the mass of the following. a) A spider c) A bicycle b) A nickel d) A box of cereal Solution: a) Milligrams c) Kilograms b) Grams d) Grams

Volume and Mass of Water Volume in Cubic Units 1 m3 = 1 kL = 1 t (1000 kg) 1 dm3 = 1 L = 1 kg 1 cm3 = 1 mL = 1 g Mass of Water Volume in Liters

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.

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

Temperature The term degrees Celsius (ºC) is used to measure temperature. Water boils 212ºF 100ºC Body temperature 98.6ºF 37ºC Comfortable room 71.6ºF 22ºC Water freezes 32ºF 0ºC Description ºF ºC Temperature

A Celsius rhyme Thirty is hot, Twenty is nice. Ten is cold, Zero is ice.

Example: Choose ºF or ºC The temperature of a can of frozen juice about 2 __. The temperature of a person with a fever is about 101.5 __. The temperature of a bowl of hot soup is about 175 __. Solution: a) ºC b) ºF c) ºF

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

Example: Conversions The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer? Solution: The equivalent temperature is about 29.4ºC.

Example: Conversions The temperature of a cold glass of milk is about 5ºC . What is the equivalent temperature on the Fahrenheit thermometer? Solution: The equivalent temperature is about 41ºF.

Temperature conversion application Earlier we said that, “Ten is cold.” What Fahrenheit temperature is the same as 10 degree Celsius?

Dimensional Analysis and Conversions to and from the Metric System 5.4 Dimensional Analysis and Conversions to and from the Metric System

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:

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

Example: Using Dimensional Analysis A recipe calls for 8 cups of blueberries. How many pints is this? Solution: Convert 75 miles per hour to inches per minute.

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)

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)

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)

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)

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)

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 14.25 in2. What is its area in square centimeters?

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 38.75 mi, 62 kph is equivalent to 38.75 mph.

Application: Driving in Canada When driving in Canada, the price of gasoline is priced in dollars per liter. On June 14, 2010, the average price of gasoline in Canada was $0.995 per liter. What was the cost per gallon of gasoline on that date?

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 73.92 mg.