Chapter 5 The Metric System

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 to the left To change from a larger unit to a smaller unit move the decimal point to the right

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.

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.

Volume 1 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL Volume in Liters Three dimensions: Length Width Height 1 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL Volume in Liters Volume in Cubic Units

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:

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 = 1g 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.

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

Example: Conversions The equivalent temperature is about 29.4ºC. 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.

Dimensional Analysis 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:

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.