Welcome to MM150! Kirsten Meymaris Unit 5 Plan for the hour MML Challenge!! Basic Terms in Metric System (5.1) Length, Area, Volume (5.2) Mass and Temperature (5.3) Conversions To and From Metric System (5.4)

MML Challenge!! Everyone score 60/60 this week, Unit 5?! Challenge: Can everyone get 60/60 on your MML Graded Practice this week?!  REMEMBER: 1- You can go in and out of the MML all Unit long (through next Tuesday at midnight) 2 - You can keep trying similar problems until you get that one right 3 – You can view an example of this problem being worked out 4 - You can step through this problem getting feedback at each step 5 – You can send me an email with your questions about this problem.

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

Basic Terms Common Use US Customary Metric System Length inch foot, yard mile centimeter meter kilometer Area inch2 feet2,yard2 acre cm2 meter2 hectare Volume (solid) inch3 foot3 yard3 cm3 meters3 Volume (non-solid, liquid) ounce, cup quart gallon milliliter, cc liter Weight/Mass* ounce pound (lb) ton gram kilogram tonne Temperature Fahrenheit Celsius * Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.

Metric Prefixes Count how many prefixes/decimal places to move tera giga mega kilo hecto deka * deci centi mili micro nano pico 1012 109 106 103 102 101 1 10-1 10-2 10-3 10-6 10-9 10-12 tera giga mega kilo hecto deka * deci centi mili micro nano pico 1012 109 106 103 102 101 1 10-1 10-2 10-3 10-6 10-9 10-12 Count how many prefixes/decimal places to move Put in decimal point (if not already there) Move decimal point to the left/right (adding zeros where necessary) Smaller to larger? (Left = L ~ Larger) Larger to smaller? (Right = R ~ Smaller)

Example: Changing Units within Metric System Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MB

Metric Prefixes BASE tera giga mega kilo hecto deka * deci centi mili micro nano pico 1012 109 106 103 102 101 1 10-1 10-2 10-3 10-6 10-9 10-12

Example: Changing Units within Metric System Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MB Solutions: 54.6 m = 0.0546 km. 0.89 kg = 89,000 cg 1.5 TB = 1,500,000 MB

5.2 Length, Area, and Volume

Common Use US Customary Metric System Length inch foot, yard mile centimeter meter kilometer Area inch2 feet2,yard2 acre cm2 meter2 hectare Volume (solid) inch3 foot3 yard3 cm3 meters3 Volume (non-solid, liquid) ounce, cup quart gallon milliliter, cc liter Weight/Mass* ounce pound (lb) ton gram kilogram tonne Temperature Fahrenheit Celsius * Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.

Length The meter is used to measure things that we normally measure in yards and feet. Area Areas are always expressed in square units. Common Formulas:

Area 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 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 in the Metric System 1 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL Volume in Liters Volume in Cubic Units cc = cubic centimeters = 1cm3 Common Formulas:

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?

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:

5.3 Mass and Temperature

Common Use US Customary Metric System Length inch foot, yard mile centimeter meter kilometer Area inch2 feet2,yard2 acre cm2 meter2 hectare Volume (solid) inch3 foot3 yard3 cm3 meters3 Volume (non-solid, liquid) ounce, cup quart gallon milliliter, cc liter Weight/Mass* ounce pound (lb) ton gram kilogram tonne Temperature Fahrenheit Celsius * Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.

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.

Mass Weight Mass Earth Moon

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 A fish tank is 1 m long, 60 cm high and 260 mm wide. Determine the number of liters that the tank holds.

Example: Capacity A fish tank is 1 m long, 60 cm high and 260 mm wide. 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 Water boils 212ºF 100ºC Body temperature 98.6ºF 37ºC Comfortable room 71.6ºF 22ºC Water freezes 32ºF 0ºC Description ºF ºC Temperature

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 __.

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

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

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?

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 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.

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

Dimensional Analysis Examples of unit fractions:

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 fluid ounce (fl oz) ≈ 30 milliliters (ml) 1 quart (qt) ≈ 0.95 liter (l) 1 gallon (gal) ≈ 3.8 liters (l) 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? The area of a box is 14.25 in2. What is its area in square centimeters?

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.

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.

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?

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.

Remember to Ask, Ask, Ask! kmeymaris@kaplan.edu AIM: kkmeymaris