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2.03 Basic Unit of Measurement and the

Dr. Fred Omega Garces 152 Miramar College

1 2.03 Basic Unit of Measurement and the Metric System 05.2015 Measurements In 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 Science

Scientist make countless measurement during their experiment to prove or disprove theory.

2 2.03 Basic Unit of Measurement and the Metric System 05.2015 Numbers without meaning

What is your response if I told you that I weigh 64.4 You would either think I was mad or anorexic.

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

3 2.03 Basic Unit of Measurement and the Metric System 05.2015 System of Measurements

What units are used? Scientific Community The Rest of the World America

English System Metric System 1 ft = 12 in 1 km = 1000 m Le System 1 yd= 3 ft 1 m = 100 cm International d’Unites 1 mi. = 1,760 Yd 1 m = 1•109 nm time g sec 1 mi = 5280 ft length g m g kg temperature g

4 2.03 Basic Unit of Measurement and the Metric System 05.2015 Units – gives meaning to the measurement What are Units ? Standards used for quantitative comparison. Rest of the World i.e., Ft, mi, in, cm, mi/hr, km/min, gal, J, cal uses the metric system. The U.S. prefers the English Unit system.

5 2.03 Basic Unit of Measurement and the Metric System 05.2015 Metric system and the Le 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

6 2.03 Basic Unit of Measurement and the Metric System 05.2015 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:

Quantity( Unit( Symbol( length( meter( m( mass( ( kg( time( ( s( temperature( kelvin( ( amount( ( mol( electric(current( ( A( luminous(intensity( ( cd(

All others units are derived units

7 2.03 Basic Unit of Measurement and the Metric System 05.2015 Derived SI Units

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

Derived Units i.e., (L or mL) = Length x Length x Length cm x cm x cm = cm3 = cc = mL

Newton (N) (mass x length) / time2 (kg x m) / s2 = N

8 2.03 Basic Unit of Measurement and the Metric System 05.2015 Ease of conversion of the SI units Prefix multipliers

The SI units employ a series of prefix to indicate fraction or multiple of units.

Prefix Symbol exp factor factor Mega M 10 6 1,000,000 kilo k 10 3 1,000 deci d 10 -1 1 / 10 centi c 10 -2 1 / 100 milli m 10 -3 1 / 1,000 - 6 micro m 10 1 /1 ,000,000 nano n 10 -9 1 / 1,000,000,000 pico p 10 -12 1 / 1,000,000,000,000

9 2.03 Basic Unit of Measurement and the Metric System 05.2015 Relationship Consider the relationship between each metric prefix. Prefix Fraction Decimal Exponential Conversion Tera 1 000 000 000 000 1 000 000 000 000 1 • e12 1 000 000 000 000 m = 1 Tm Giga 1 000 000 000 1 000 000 000 1 • e9 1 000 000 000 m = 1 Gm Mega 1 000 000 1 000 000 1 • e6 1 000 000 m = 1 Mm kilo 1000 1000 1 • e3 1 000 m = 1km - 1 1 1 1m = 1m deci 1/10 0.1 1 • e-1 1m = 10 dm centi 1 / 100 0.01 1 • e-2 1m = 100 cm milli 1 / 1000 0.001 1 • e-3 1m = 1000 m micro 1/1 000 000 .000 001 1 • e-6 1m = 1 000 000 m nano 1/1 000 000 000 .000 000 001 1 • e-9 1m = 1 000 000 000 m pico 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 (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.

10 2.03 Basic Unit of Measurement and the Metric System 05.2015 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 inches To solve this problem the relationship between miles and inches must be known. In fact to convert between miles, yards, feet and inches each relationship (conversion factor) must be known. Length 1 Mi. = 1,760 yd = 5,280 ft = 63,360 in 1 yards = 3 ft = 36 in Therefore in 26 miles, there are : 63,360 in 26 mile ∗ = 1,647,360 = 1.6 million inches 1 mile

11 2.03 Basic Unit of Measurement and the Metric System 05.2015 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, you simply need to know that kilo means 1000, therefore there are 1000m = 1 km (conversion factor) and that there are 100 cm = 1 m Kilometers n meters n centimeters This 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:

1000&m 100&cm 100#km#∗# ∗# = #1•107 #cm 1&km 1&m

12 2.03 Basic Unit of Measurement and the Metric System 05.2015 English and Metric System. In science, measurement is based on the metric system (SI). Life in America is a more complicated because we live in a global world that uses the metric system but at home we use the English 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.

13 2.03 Basic Unit of Measurement and the Metric System 05.2015 Other Metric relationship (Exact Definitions). Length - distance

English Metric English - Metric 1 ft = 12 in 1 km = 1000 m 1 in = 2.54 cm 1 yd= 3 ft 1 m = 100 cm 1 mi. = 1.609 km 1 mi. = 1,760 yd. 1 m = 1•109 nm

Volume - space English Metric English - Metric 1 gal = 4 qt 1 L = 1000 ml 1 gal = 3.785 L 1 qt = 2 pt 1 ml = 1 cm3 = 1 cc 1 fl oz = 29.57 ml 1pt = 16 fl oz.

Mass - quantity of matter

English Metric English - Metric 1 lb. = 16 oz 1 kg = 1000 g 1 lb. = 453.6 g 1 Ton = 2000 lb. 1 g = 1000 mg 1 kg = 2.205 lb.

14 2.03 Basic Unit of Measurement and the Metric System 05.2015 Some interesting measurements

Order of magnitude as expressed via metric measurements

15 2.03 Basic Unit of Measurement and the Metric System 05.2015 Putting it in perspective

In 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.

Length Volume Mass English - Metric English - Metric English - Metric miles - km gallons - Liters pounds - kg

Distance of one light 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

16 2.03 Basic Unit of Measurement and the Metric System 05.2015 Summary

Measurement - 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 Conversion Tera 1 000 000 000 000 1 000 000 000 000 1 • e12 1 000 000 000 000 m = 1 Tm Giga 1 000 000 000 1 000 000 000 1 • e9 1 000 000 000 m = 1 Gm Mega 1 000 000 1 000 000 1 • e6 1 000 000 m = 1 Mm kilo 1000 1000 1 • e3 1 000 m = 1km - 1 1 1 1m = 1m deci 1/10 0.1 1 • e-1 1m = 10 dm centi 1 / 100 0.01 1 • e-2 1m = 100 cm milli 1 / 1000 0.001 1 • e-3 1m = 1000 m micro 1/1 000 000 .000 001 1 • e-6 1m = 1 000 000 m nano 1/1 000 000 000 .000 000 001 1 • e-9 1m = 1 000 000 000 m pico 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

17 2.03 Basic Unit of Measurement and the Metric System 05.2015 Sample Questions

1. 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 1. C

2. Which of the following has three (3) significant figures: a) 0.006 b) 160 c) 1.09e3 d) 1019. 2. C

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) 3. B a) 16.4 b) 1.00 c) 106 d) 6.45

4. How many centimeters are there in 1-kilometer ? 4. D a) 100 b) 1e-5 c) 1000 d) 1e5

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

6. D .338oz=10cc 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? 7. C 50 g a) 41 g b) 4.2e6 ug c) 5e4 mg d) 6.1e-3 Kg

8. D 984mi/hr 8. Which is the fastest speed ? a) 100 km/hr b) 100 mi/hr c) 1e5 m/hr d) 5.2e6 ft/hr

18 2.03 Basic Unit of Measurement and the Metric System 05.2015 Sample Questions

9. 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. 9. A 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? 9. C 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 10. D , how should it be written? a) 1200 b) 250 c) 1250.4 d) 1250.38 11. C 12. How many of the following numbers have 5 significant figures: 19.000 0.010006 1.6090e8 13600 a) 1 b) 2 c) 3 d) 4 12. A

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

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 14. D

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

19 2.03 Basic Unit of Measurement and the Metric System 05.2015