nikki grantham. basic terms and conversions within the metric system

Nikki Grantham

Basic Terms and Conversions within the Metric 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.

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.

a little more than a quart

volumeLliter

about 2.2 pounds

masskgkilogram

a little more than a yard

lengthmmeter

Comparison to Customary

Common Use

Abbrev

Metric Term

1/1000 of base unit

mmilli1/100 of base unit

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

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 measure until you obtain the desired unit of measure.

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

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

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.

18,000

250= 72

a. 351,000 dm

b. 35,100 dm

c. 351 dm

d. 35.1 dm

a. 0.1 times greater

b. 10 times greater

c. 100 times greater

d. 1000 times greater

Length, Area, and Volume

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.

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.

A=82.5m x 25.4 mA=2095.5m2

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 LitersVolume in Cubic Units

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?

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.

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

Solution:

V r 2h

V 3.14 3 2 12

V 339.12 cm3

V 339.12 mL

Mass and Temperature

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.

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.

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

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 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

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

Solution:V = l x w x h (Volume = length x width x height)

V = 1m x 0.26m x 0.6m

V = 0.156 m3

Since 1 m3 of water = 1 kL of water, 0.156 m3 = 0.156 kL, or 156 liters of water

A fish tank is 1 m long, 60 cm high and 260 mm wide.

Question:What is the mass of the water in kilograms?

Solution:Since 1L = 1 kg, 156 L = 156 kg of water.

The term degrees Celsius (ºC) is used to measure temperature.

Water boils212ºF100ºCBody temperature98.6ºF37ºC

Comfortable roomtemperature

71.6ºF22ºCWater freezes32ºF0ºCDescriptionºFºC

Temperature

The temperature of a can of frozen juice is 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

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

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 29.4ºC.

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.

F 9

5C 32

F 9

55 32

F 9 32

F 41

a. 80º C

b. 20º C

c. 140º C

d. Can’t determine.

Dimensional Analysis and Conversions to and from the Metric System

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:

16 oz

1 lb

1 hr

60 min

12 in.

1 ft

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 quarts

1 yard = 3 feet

1 quart = 2 pints1 foot = 12 inches

U.S. Customary Units

A recipe calls for 8 cups of blueberries. How many pints is this?

Solution:

Convert 75 miles per hour to inches per minute.

Solution:

8 cups = 8 cups 1 pint

2 cups

4 pint s

75mi

hr 75

mi

hr

5280ft

1 mi

12 in

1 ft

1 hr

60 min

75 5280 12

60

in

min = 79,200

in

min

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)

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)

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)

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)

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)

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?

Solution:

´ =3.8

22.6 gal 85.88 lgal

14.25 in2 6.5 cm2

1 in2

92.625 cm2

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.

62 km

1 mi

1.6 km

62

1.6mi 38.75 mi

A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the baby’s weight, what dosage should be given?

Solution:

The dosage of the medication is 73.92 mg.

8 lbs 16 oz

1 lb

4 oz 128 oz 4 oz 132 oz

132 oz28 g

oz

1 kg

1000 g

20 mg

1 kg

73.92 mg

a. 3000 cm2

b. 50 m2

c. 300 m2

d. Can’t determine.

a. 1000 times greater

b. 10,000 times greater

c. 100,000 times greater

d. 1,000,000 times greater

a. 15.2 l

b. 1.052 l

c. 4 l

d. 16 l

a. 7.5 km

b. 19.2 km

c. 24 km

d. 60 km

a. 84.44º C

b. 48.89º C

c. 248º C

d. 273.6º C

a. 35º F

b. 70.56º F

c. 228.6º F

d. 203º F

nikki grantham. basic terms and conversions within the metric system

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