MEASUREMENT Units of Measurement : SI unit and derived units Unit prefixes Unit conversion using dimensional analysis Scientific notation Increment, Accuracy, Precision

OBJECTIVES Distinguish between a number and a quantity. Name SI units for length, mass, time, temperature, volume and density. Define and identify base units; unit conversions; identify prefixes Perform unit conversion using dimensional analysis.

Units of Measurement In our daily lives we deal with making measurements 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, pharmacists- Doctors and nurses make measurements constantly. Measurements like pulse rate, blood pressure, temperature, drug dosage. Math - The language of Science Scientists make countless measurements during their experiments to prove or disprove a theory.

Otherwise, it is meaningless! Units of Measurement What is your response if I told you that: I weigh 65 In any measurement magnitude (the number) as well as the unit (meaning) must be stated. Otherwise, it is meaningless!

Number vs. Quantity Quantity : number + unit UNITS MATTER!!

Systems of Measurement Scientific Community What units are used? The Rest of the World America English System 1 ft = 12 in 1 yd= 3 ft 1 mi. = 1,760 Yd 1 mi = 5280 ft Metric System 1 km = 1000 m 1 m = 100 cm Le System International d’Unites SI Units are basically an updated form of the metric system.

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. For example for: *Length we use only meter, in the US we use foot, yard, inch. *Mass we use Kg not pound. All the Prefixes are multiples of 10.

SI Units Quantity Symbol Base Unit Abbrev. Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K n mol Amount of particles mole

SI Prefix Conversions Prefix Symbol Factor Giga Mega- G 109 106 Kilo- k 103 Hecto- h 102 Deka- da 10 BASE UNIT --- 1 deci- d 10-1 centi- ? milli- m 10-3 micro-  10-6

Derived Units: Combination of base units Area ( m2) length  length = m x m Volume (m3) length  length  length= m x m x m D = M V Density (g/cm3) mass per volume

Temperature A measure of how hot or how cold an object is. SI Unit: the kelvin ( K ) Note: not a degree Absolute Zero= 0 K

Temperature Scales

Celsius and Kelvin K= oC + 273

Unit conversion using dimensional analysis Page Unit 1 - MEASUREMENT Unit conversion using dimensional analysis Page

SI Prefix Conversions To the left or right? 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

SI Prefix Conversions Prefix Symbol Factor Giga Mega- G 109 M Kilo- K 106 Kilo- K 103 Hecto- H 102 Deca- D 10 BASE UNIT --- 1 move left move right deci- d 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6

SI Prefix Conversions 1) 20 cm = ___________ m 2) 0.032 L = ______________ mL 3) 45 m = ______________ cm 4) 80.5 km = ______________ m

How would you convert 2h 45 min to second Convert 55.00 km/h to m/s

Converting by using Dimensional Analysis Steps: Identify starting ( also called given, old )& ending ( target, new) units. 2. Line up conversion factors so units cancel.( hint : the new units should on the top) 3. Multiply all top numbers & divide by each bottom number. ( ) 4. Check units & answer.

Converting by using Dimensional Analysis: inch to cm Identify 10.0 in We start by writing down the Given (old) and its Unit

Converting by using Dimensional Analysis: inch to cm Line up 10.0 in x 2.54 cm 1 in We know 1 in = 2.54 cm. So our conversion factor is : 1 in = 2.54 cm. Since we want to convert to cm, it goes on the top. ( Hint)

Converting by using Dimensional Analysis: inch to cm Cancel units 10.0 in x 2.54 cm 1 in Now we cancel and collect units. The inches cancel out, leaving us with cm : the Target unit.

Converting by using Dimensional Analysis: inch to cm 10.0 in x 2.54 cm 25.4 cm = 1 in Since the unit is correct, all is left to do the math ... The Answer

Lets check it out !!!!!! Find the 10 in mark and directly across at the cm side. What number do you find?

Converting by using Dimensional Analysis: inch to cm You go to Europe and decide to have a haircut. Your hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? Identify , line up, cancel out, multiply, check 8.0 cm 1 in 2.54 cm = ? in Question: Is the conversion Factor the same? What’s the difference?

Converting by using Dimensional Analysis: g to Kg Convert 250 g into Kg Identify , line up, cancel out, multiply, check 250 g x 1Kg = Kg 1000 g

Converting by using Dimensional Analysis: Kg to g Convert 1.5 Kg into g Identify : Given and Target unit Line up: Conversion Factor 1.5 kg x = g Q: Which conversion factor will you be using? 1Kg = 1000g or 1000g= 1Kg

A more complex conversion km to m hr s kilometers into meters and hour into second. We can do both conversions at once using the same method as in the previous conversion.

A more complex conversion km to m hr s Identify 80 km Write down the _____and ____ hr

A more complex conversion km to m Line up 80 km x hr s 1 hr hr 3600 s First conversion factor is: 1 hour = 3600 sec.

A more complex conversion km to m Line up 80 km x hr s 1 hr x 1000 m hr 3600 s 1 km The second conversion factor is: 1 km = 1000 m.

A more complex conversion km to m Cancel out units 80 km x hr s 1 hr x 1000 m m = s hr 3600 s 1 km Check your units !!! If you have chosen the correct conversion factors, you should only be left with the units you want to convert to.

A more complex conversion km to m hr s 80 km x 1 hr x 1000 m = hr 3600 s 1 km 80,000 m m The Answer!! = s 3600 s

A Very more complex conversion to finish at home today !! Problem1:Convert 1 year into seconds year seconds 1y = s 1 y 365 days 24h 1day 1 h 60s

Dimensional Analysis Problem2: Taft football needs 550 cm for a 1st down. How many yards is this? cm yd 550 cm = yd 1 yd 3 ft 1 in 2.54 cm 12in 1ft

Dimensional Analysis cm pieces 1.3 m = pieces Problem3: A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? cm pieces 1.3 m = pieces

Dimensional Analysis Problem5:How old are you in minutes? Age in y

How would you convert 2h 45 min to second Homework Units and Conversions HW Due: tomorrow How would you convert 2h 45 min to second Convert 55.00 km/h to m/s

M x 10n Scientific Notation M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10

Other Examples: 5.45E+6 5.45 x 10^6

Numbers less than 1 will have a negative exponent. Numbers bigger than 1 will have a positive exponent. A millionth of a second is: 0.000001 sec 1.0E-6 1.0x10^-6

Limits of Measurement Accuracy and Precision

Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: Accuracy Who is more accurate (Susan or Amy) when measuring a book that has a true length of 17.0cm? Susan: 18.1cm, 16.0cm, 18.0cm, 17.1cm Amy: 16.5cm, 16.0cm, 16.2cm, 16.3cm

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is regardless is it is close to the real value.

Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Example: Evaluate whether the following are precise, accurate or both. Not Precise Not Accurate Precise Accurate Precise

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