2.02 units and the metric system - san diego miramar...

1 January 102.02 Units and the Metric System

2.02 Units and the Metric System

Dr. Fred Omega GarcesChemistry 100

Miramar College


MeasurementsIn our daily lives we deal with making measurement routinely.

i.e., How much gasoline is required to fill your gas tank? What time did you wake up this morning? How fast did you drive to school today ?

Doctors, nurses, pharmacist-Doctors and nurses make measurement constantly. Measurements like pulse rate, blood pressure, temperature, drug dosage.

Math - The language of ScienceScientist make countless measurement during their experiment to prove or disprove theory.


Numbers without meaningWhat is your response if I told you that

I weigh 64.4You would either think I was mad or anorexic.

In any measurement Magnitude (the number) as well as Unit (meaning) must be stated.Otherwise it is Meaningless


System of Measurements

Scientific Community

The Rest of the World

America

English System1 ft = 12 in1 yd= 3 ft1 mi. = 1,760 Yd1 mi = 5280 ft

Metric System1 km = 1000 m1 m = 100 cm1 m = 1•109 nm

Le SystemInternational d’Unites

time g seclength g mmass g kgtemperature g Kelvin

What units are used?


Units – gives meaning to the measurementWhat are Units ?Standards used for quantitative comparison.

i.e., Ft, mi, in, cm, mi/hr, km/min, gal, J, calThe U.S. prefers the English Unit system.

Rest of the World uses the metric system.


Metric system and theLe Systeme International d'Unites (SI)

The Metric system is convenient because it uses only one fundamental unit for each type of measurement, and all of its conversion factors are multiples of 10.

The scientific community uses an updated metric plan called the SI units.SI (Le Systeme International d'Unites)

There are seven (7) quantities in which all units can be derived, this is the basis of the SI units; all other units are derived from these seven


SI units There are seven quantities (fundamental) in which all units can be derived; these are the base units and the SI defines these as:

All others units are derived units


Relationship of

SI to SI Derived

Units

Relationships of the SI units to SI derived units with special names


What are Derived Units ?Derived units result from these seven base units.

i.e., vol. (L) derived from m3 g meters.energy (J) derived from N•m or (kg•m / s2) • mpressure (psi) derived from lb. /in2 or (kg /m2)


Ease of conversion of the SI unitsThe SI units employ a series of prefix to indicate

decimal fraction or multiple of units.

Prefix Symbol exp factor factorMega M 10 6 1,000,000kilo k 10 3 1,000deci d 10 -1 1 / 10centi c 10 -2 1 / 100milli m 10 -3 1 / 1,000

micro m 10- 6 1 /1 ,000,000nano n 10 -9 1 / 1,000,000,000pico p 10 -12 1 / 1,000,000,000,000


Metric Prefix RelationshipConsider the relationship between each metric prefix.

Prefix Fraction Decimal Exponential ConversionTera 1 000 000 000 000 1 000 000 000 000 1 • e12 1 000 000 000 000 m = 1 TmGiga 1 000 000 000 1 000 000 000 1 • e9 1 000 000 000 m = 1 GmMega 1 000 000 1 000 000 1 • e6 1 000 000 m = 1 Mmkilo 1000 1000 1 • e3 1 000 m = 1km- 1 1 1 1m = 1m

deci 1/10 0.1 1 • e-1 1m = 10 dmcenti 1 / 100 0.01 1 • e-2 1m = 100 cmmilli 1 / 1000 0.001 1 • e-3 1m = 1000 m

micro 1/1 000 000 .000 001 1 • e-6 1m = 1 000 000 mnano 1/1 000 000 000 .000 000 001 1 • e-9 1m = 1 000 000 000 mpico 1/1 000 000 000 000 .000 000 000 001 1 • e-12 1m = 1 000 000 000 000 m

femto 1/1 000 000 000 000 000 .000 000 000 000 001 1 • e-15 1m = 1 000 000 000 000 000 m

In using the metric system conversion factor in dimensional analysis

remember to use the conversion ratio that makes sense. For example the

conversion between micrograms (µg) and grams (g) is either 1 µg = 1•10-6 g

or 1,000,000 µg = 1g. It is easier to use the 1,000,000 µg = 1g conversion

since this conversion does not involve negative exponents.


Conversion within English System

In the English system, exact conversion factors must be known.i.e., How many inches in a marathon (26 miles 385 yards)? To solve this, must know that there are 63,360 in = 1 mile

Mile n Yard n feet n inchesTo solve this problem the relationship between miles and in must

be known. In fact to convert between miles, yards, feet and inches each relationship (conversion factor) must be known.

Length1 Mi. = 1,760 yd = 5,280 ft = 63,360 in

1 yards = 3 ft = 36 in

Therefore in 26 miles, there are :

26 mile ∗ 63,360 in1 mile

= 1,647,360 = 1.6 million inches


Conversion within Metric System.Advantage of the metric system is that converting from one unit to

the other is just a matter of multiplying or dividing by 10's.i.e., How many centimeters in a 100 km ? To solve this, simply need to know that kilo means 1000, therefore

there are 1000m = 1 km (conversion factor) and that there are 100 cm = 1 mKilometers n meters n centimetersThis is very useful in science, especially when you have to work

numerical problems.Length

1 km = 1000 m, 1 m = 100 cm

Therefore 100 km is equal to:

€

100 km ∗ 1000 m1 km

∗ 100 cm1 m

= 1 • 107 cm


English and Metric System.

The metric system (or SI) is very useful in science, especially when you have to work numerical problems. When dealing with the metric system the conversion is easy.

When dealing with English and metric, the conversion factor between two units must be known: i.e., 1 inch = 2.54 cm

In the automotive industry, the U.S. still uses

predominately the English system. If you want a wrench for

example that is the next size smaller than a 7/16 -inch, it

would be logical to use 6/16-inch. The correct next lower

size is actually labeled 6/16-inch. It becomes really

complicated if you are looking for the next smaller size for

3/4-inch because it is not 2/4 (or 1/2-inch) it is actually

11/16-inch -go figure.

In science, measurement is based on the metric system (SI). Life in America is a bit more complicated because we live in a global world that uses the metric system but at home we use the English system.


Other Metric relationship.Length - distance

English1 ft = 12 in1 yd= 3 ft1 mi. = 1,760 yd.

Metric1 km = 1000 m1 m = 100 cm1 m = 1•109 nm

Volume - spaceEnglish

1 gal = 4 qt1 qt = 2 pt1pt = 16 fl oz.

Metric1 L = 1000 ml1 ml = 1 cm3 = 1 cc

Mass - quantity of matterEnglish

1 lb. = 16 oz1 Ton = 2000 lb.

Metric1 kg = 1000 g1 g = 1000 mg

English - Metric1 in = 2.54 cm1 mi. = 1.609 km

English - Metric1 gal = 3.785 L1 fl oz = 29.57 ml

English - Metric1 lb. = 453.6 g1 kg = 2.205 lb.


Some interesting measurements

Order of magnitude as expressed via metric measurements


Putting it in perspectiveIn class you will be assigned a conversion project. It will be up to you to make the

appropriate conversion. Be prepared to make a presentation on this assignment. You can

create a poster, a PowerPoint slide show or come up with something creative.

LengthEnglish - Metric

miles - km

VolumeEnglish - Metricgallons - Liters

MassEnglish - Metric

pounds - kg

Distance of one light year Volume of space in universe Mass of universe

Distance around the world. Volume of the sun Mass of sun, Jupiter, Earth, Moon

Distance San Diego to NY City. Volume of earth Mass of water in ocean

Distance SD to LA. Volume of water in ocean Mass of Empire State Building.

Distance Pet Co to Qualcomm. Volume of water in great lakes Mass of Statue of Liberty.

1000 mi to km volume of water in Shamu's pool Mass of average elephant.

500 mi to km volume of water in Miramar's pool 1 ton g kg

100 mi to km Volume of gasoline in Hummer 300 lb

60 mi to km Volume of water in 21 gallon tank 150 lb

25-mi to km volume of air in lungs 100 lb

10 mi to km volume in 1 gallon 50 lb


SummaryMeasurement - Measurement

Consist of a Magnitude (a number) and a Unit (the meaning)

Unit system - Le Systeme International d'Unites ( SI ) There are three unit systems. The English, Metric and SI (Le Systeme International d'Unites). The SI is derived from the metric and is more specific.

The Metric system is based on prefixes which relates the magnitude of a number to another by factors of 10.

Prefix Fraction Decimal Exponential ConversionTera 1 000 000 000 000 1 000 000 000 000 1 • e12 1 000 000 000 000 m = 1 TmGiga 1 000 000 000 1 000 000 000 1 • e9 1 000 000 000 m = 1 GmMega 1 000 000 1 000 000 1 • e6 1 000 000 m = 1 Mmkilo 1000 1000 1 • e3 1 000 m = 1km- 1 1 1 1m = 1m

deci 1/10 0.1 1 • e-1 1m = 10 dmcenti 1 / 100 0.01 1 • e-2 1m = 100 cmmilli 1 / 1000 0.001 1 • e-3 1m = 1000 m

micro 1/1 000 000 .000 001 1 • e-6 1m = 1 000 000 mnano 1/1 000 000 000 .000 000 001 1 • e-9 1m = 1 000 000 000 mpico 1/1 000 000 000 000 .000 000 000 001 1 • e-12 1m = 1 000 000 000 000 m

femto 1/1 000 000 000 000 000 .000 000 000 000 001 1 • e-15 1m = 1 000 000 000 000 000 m


Sample Questions1. Which one of the following measurements contains four significant figures ?a) 0.0030 g b) 120340 g c) 900300 g d) 40.000 e4 g

2. Which of the following has three (3) significant figures:a) 0.06 b) 1600 c) 1.090e3 d) 19.00

3. One edge of a cube is measured and found to be 2.54 cm. What is the volume of the cube in in3. (1.00 in = 2.54 cm)

a) 16.4 b) 1.00 c) 106 d) 6.45

4. How many centimeters are there in 1 kilometer ?a) 100 b) 1e-5 c) 1000 d) 1e6

5. At what temperature does K = °Ca) 100 b) 0 c) 273 d) Never the same

6. The prescribed injection of a drug is 0.338 oz. If the syringe is graduated in cubic centimeters, to what mark would you draw the drug? (29.6 mL = 1 oz)a) 5.00cc b) 0.34 cc c) 0.0114 cc d) 10.0 cc

7. Which of the following is the largest mass?a) 41 g b) 8.2e6 mg c) 3e3 mg d) 4.1e-8 Kg

8. Which is the fastest speed ?a) 100 km/hr b) 100 mi/hr c) 1e5 m/hr d) 5.2e6 ft/hr


Sample Questions9. The lethal dose of heroine is 150 mg per kilogram of body weight.

Estimate how many grams of heroin would be lethal for a 200-lb man.a) 13.6 g b) 13.6 mg c) 13.6 oz d) .0136 lb

10. You obtain the number 1250.37986 on a calculator. If this number actually has four (4) significant figures, how should it be written?a) 1251 b) 1250.3799 c) 1.250e3 d) 1.250e-3

11. You obtain the number 1250.37986 on a calculator. If you need to round this number to the hundredths, how should it be written?a) 1200 b) 250 c) 1250.4 d) 1250.38

12. How many of the following numbers have 5 significant figures:19.000 0.010006 1.6090e8 13600a) 1 b) 2 c) 3 d) 4

13. The number 6.33e-2 equals :a) 0.0633 b) 0.633 c) 633. d) 63.3

14. When expressed in exponential notation, the number 0.000302 becomes:a) 3.02e-4 b) 3.02e4 c) 3.02e3 d) 3.02e-3

15. A woman who weights 38.5 Kg is most likely to be which of the following ?a) a basketball center b) a discus thrower c) a gymnast d) a volleyball player

16. Which of the following is the shortest length ?a) 1.21m b) 75 in c) 3 ft - 5 in d) a yard stick

2.02 units and the metric system - san diego miramar...

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