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**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)

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**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 with your questions about this problem.

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

5.1 Basic Terms and Conversions within the Metric System

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**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.

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**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)

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**Example: Changing Units within Metric System**

Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MB

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**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

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**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 = km. 0.89 kg = 89,000 cg 1.5 TB = 1,500,000 MB

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5.2 Length, Area, and Volume

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**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.

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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:

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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.

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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.

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**Volume in the Metric System**

1 m = kL 1 dm = L 1 cm = mL Volume in Liters Volume in Cubic Units cc = cubic centimeters = 1cm3 Common Formulas:

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**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?

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**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:

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5.3 Mass and Temperature

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**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.

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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.

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Mass Weight Mass Earth Moon

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**Volume and Mass of Water**

Volume in Cubic Units 1 m = kL = 1 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 A fish tank is 1 m long, 60 cm high and 260 mm wide.**

Determine the number of liters that the tank holds.

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**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.

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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**

Comfortable room 71.6ºF 22ºC Water freezes 32ºF 0ºC Description ºF ºC Temperature

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**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 __. The temperature of a bowl of hot soup is about 175 __.

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**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 __. The temperature of a bowl of hot soup is about 175 __. Solution: a) ºC b) ºF c) ºF

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Conversions

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

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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.

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

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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.

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

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.

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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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Dimensional Analysis Examples of unit fractions:

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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 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)

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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? The area of a box is in2. What is its area in square centimeters?

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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.

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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?

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

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