Welcome to Survey of

Mathematics

Unit 5 – The Metric System

Agenda

• Miscellania• Prefixes and what they mean• Measures of Length• Measuring Volume• Measuring Mass & Weight• Measuring Temperature• What else could there be?• Wrapping up

I said the metric system is the tool of the devil... My car gets 40 rods to the hog's head, and that's the way I likes it!" ...

How do we measure things?

1 pint = 2 cups 1 year = 365 days1 cup (liquid) = 8 fluid ounces

1 day = 24 hours1 ton = 2000 pounds

1 hour = 60 minutes

1 pound = 16 ounces

1 minute = 60 seconds

1 mile = 5280 feet

1 gallon = 4 quarts1 yard = 3 feet

1 quart = 2 pints1 foot = 12 inches

U.S. Customary Units

How Big is a Meter?

• Basic metric measurement = 1 Meter

A doorknob is typically about 1 m high

A meter stick is just under 40 inches long, a few inches longer than a yard stick.  A meter is a typical height for a 3-year old child, or about the size of two cocker spaniels.

Source: http://lamar.colostate.edu/~hillger/common.html

Metric Prefixes

1/1000 of base unit

mmilli1/100 of base unit

ccenti1/10 of base unitddecibase unit10 base unitdadeka100 base unithhecto1000 base unitkkiloMeaningSymbolPrefix

Measuring Length

• Millimeters - mm• Centimeters - cm• Decimeters – dm• Meters – m• Dekameters –

dam• Hectometers – hm• Kilometers - km

A millimeter (mm) is about the thickness of a dime.  The smallest marks on a meter stick are 1 mm apart.   There are 1,000 millimeters in a meter

The diameter of a CD or DVD is 12 cm

The world's longest suspension bridge, Akashi Kaikyo Bridge, is just under 2 kilometer (km) long, measuring 1,991 m. It would take you approximately 23 minutes to walk across this bridge.

Converting within SI (Metric) Units

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.

Example: How many centimeters is 2.5 meters?Answer: 1 meter has 100 centimeters in it, so move the

decimal two places to the right … 2.50 m = 250 cm

1 km 1 hm 1dam base 1 dm 1 cm 1 mm 1000 m 100 m 10m 1m 0.1m 0.01m 0.001m

Converting from U.S. Customary Units to

Metric UnitsLENGTH

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)

Converting from U.S. Customary Units to

Metric Units• Example: It is 5 miles from my house to

where I work. How many kilometers is it?– Answer: since 1 mile (mi) ≈ 1.6 kilometers (km)

multiply (5 mi)(1.6 km / mi) = 8 km

• Example: My television has a 25 inch screen (measured along the diagonal). How many centimeters is that?– Answer: Since 1 inch (in.) ≈ 2.54 centimeters

(cm), multiply (25 in)(2.54 cm/in) = 63.5 cm

Volume, Mass & Weight

• Volume – base units: Liters• Mass (weight) – base units: grams

1 liter of water weighs 1 kilogram, so 1 cubic meter — 1000 liters — of water weighs 1000 kilograms or 1 metric ton.

A US cent weighs exactly 2.5 g, while the nickel weighs exactly 5 g

Source: http://lamar.colostate.edu/~hillger/common.html

Volume• There are 1000 milliliters

(mL) in one LiterNote: the 500 ml size bottle water is arguably the most popular size sold. How many ounces is that? Answer: 1 ounce (oz) ≈ 28 grams (g), so divide:(500 ml)(28 ml/oz) = 17.59 oz

• One cubic centimeter (cc) = One milliliter (mL)

500 ml Offered in 24 pack, flat cap and sport cap.

1 liter Offered in 24 pack, sport cap

www.waterboydist.com/pet.php

Volume

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?

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.

Volume and Mass of WaterVolume 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

Conversion to and from the Metric System - Volume

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 - 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)

Mass (Weight)• 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.

Mass & CapacityA 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?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.

V l w h

10.26 0.6

0.156 m3

Temperature• The term degrees Celsius (°C) is used to

measure temperature.

Water boils212°F100°C

Body temperature

98.6°F

37°C

Comfortable room

71.6°F

22°C

Water freezes32°F0°C

Description°F°C

Temperature

Temperature Conversion

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

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

F

9

5C 32

C

5

9F 32

Example: Conversions The air temperature on a warm summer

day is about 85ºF. What is the equivalent temperature on the Celsius thermometer?

• Solution:

C 5

9F 32

C 5

985 32

C 5

953

C 29.4

The equivalent temperature is about 29.4°C.

Wrap up

• We covered some basic explanation of the metric system and some conversions between the US Customary System and the Metric System

• Check into the Doc Sharing area for notes

• Have a great week!