units of measurement : si unit and derived units unit prefixes unit conversion using dimensional...

Units of Measurement : SI unit and derived units

Unit prefixes

Unit conversion using dimensional analysis

Scientific notation

Increment, Accuracy, Precision

MEASUREMENT

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.

OBJECTIVES OBJECTIVES

Units of MeasurementUnits 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.

Units of MeasurementUnits 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 MeasurementScientific Scientific

CommunityCommunityScientific Scientific

CommunityCommunityThe Rest of the The Rest of the WorldWorld

AmericaAmerica

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

Metric SystemMetric System1 km = 1000 m1 m = 100 cm

Le SystemLe SystemInternational d’UnitesInternational d’UnitesLe SystemLe SystemInternational d’UnitesInternational d’Unites

What units are used?What units are used?

SI Units are basically an updated form of the metric system.

Metric system and theMetric system and theLe Systeme International d'Unites (SI)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 Base Unit Abbrev.

Length

Mass

Time

Temp

meter

kilogram

second

kelvin

m

kg

s

K

Amount of particles mole mol

Symbol

l

m

t

T

n

SI Prefix Conversions

Giga

Mega-

G 109

deci- d 10-1

centi- ?

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

BASE UNIT --- 1

kilo- k 103

Hecto- h 102

Deka- da 10

106

Derived Units: Combination of base units

• Area ( m2)• length length = m x m

• Volume (m3) – length length length= m x m x m

D = MV

• 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

Density• An object has a volume of 825 cm3 and a

density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,200 g

V

MD

Density• A liquid has a density of 0.87 g/mL. What

volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

Unit conversion using dimensional

analysis

Page

Unit 1 - MEASUREMENT

SI Prefix Conversions

1. Find the difference between the

exponents of the two prefixes.

2. Move the decimal that many places.

To the leftor right?

SI Prefix Conversions

mo

ve l

eft

mo

ve r

igh

t

Giga

Mega-

G 109

deci- d 10-1

centi- ?

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

BASE UNIT --- 1

kilo- k 103

Hecto- H 102

Deca- D 10

106

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

• Steps:

1. 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

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

1 in

2.54 cm

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 x1 in

2.54 cm

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

1 in

2.54 cm = 25.4 cm

Since the unit is correct, all is left to do the math ...

The Answer

Converting by using Dimensional Analysis: inch to cm

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

5) 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: inch to cm

• Convert 250 g into Kg

Identify , line up, cancel out, multiply, check

250 g x 1Kg = Kg

1000 g

Converting by using Dimensional Analysis: g to Kg

• Convert 1.5 Kg into g

• Identify : Given and Target unit

• Line up: Conversion Factor

1.5 kg x = g

Converting by using Dimensional Analysis: Kg to g

Q: Which conversion factor will you be using?1Kg = 1000g or 1000g= 1Kg

A more complex conversionkm to mhr s

kilometers into meters and hour into second. We can do both conversions at once using the same method as in the previous conversion.

Identify

80 kmhr

A more complex conversionkm to mhr s

Write down the _____and ____

Line up

80 km xhr

1 hr 3600 s

A more complex conversionkm to mhr s

First conversion factor is: 1 hour = 3600 sec.

Line up

80 km x

hr

1 hr x

3600 s

1000 m

1 km

A more complex conversionkm to mhr s

The second conversion factor is: 1 km = 1000 m.

Cancel out units

80 km x

hr

1 hr x

3600 s

1000 m

1 km=

A more complex conversionkm to mhr s

Check your units !!!If you have chosen the correct conversion factors, you should only be left with the units you want to convert to.

ms

80 km x

hr

1 hr x

3600 s

1000 m

1 km=

80,000 m

3600 s=

ms

A more complex conversionkm to mhr s

The Answer!!

Problem1:Convert 1 year into seconds

yearseconds

A Very more complex conversionto finish at home today !!

1 y365 days

24h

1day

1 h

60s

1y= s

Problem2: Taft football needs 550 cm for a 1st down. How many yards is this?

550 cm

1 in

2.54 cm

= yd

cm yd

12in

1ft

1 yd

3 ft

Dimensional Analysis

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

1.3 m= pieces

cm pieces

Dimensional Analysis

Dimensional Analysis

•Problem5:How old are you in minutes?

Age in y= min

Units and Conversions HWDue: tomorrow

HomeworkHomework

How would you convert 2h 45 min to second

Convert 55.00 km/h to m/s

Scientific Notation

M x 10n

• 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.

Accurate

Not Precise

Not Accurate

Precise

Accurate

Precise

Graduated Cylinder - Meniscus