UNIT 3 MEASUREMENT

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• Scientific notation expresses numbers as a multiple of two factors: a number between 1 and10; and ten raised to a power, or exponent.

6.02 X 1023

Scientific Notation

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Scientific Notation

• When numbers larger than 1 are expressed in scientific notation, the power of ten is positive.

2500 = 2.5 X 103

• When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative.

.0025 = 2.5 X 10-3

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• Change the following data into scientific notation.

A. The diameter of the Sun is 1 392 000 km.

Convert Data into Scientific Notation

B. The density of the Sun’s lower atmosphere is 0.000 000 028 g/cm3.

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• Move the decimal point to produce a factor between 1 and 10. Count the number of places the decimal point moved and the direction.

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• Remove the extra zeros at the end or beginning of the factor.


• Remember to add units to the answers.

MEASUREMENT

Measuring

• The numbers are only half of a measurement.

• It is 3 long.

• 3 what.

• Numbers without units are meaningless.

• How many feet in a yard?

• 3 ft

• You always need a numerical and unit value!

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• In 1795, French scientists adopted a system of standard units called the metric system.

• In 1960, an international committee of scientists met to update the metric system.

• The revised system is called the Système Internationale d’Unités, which is abbreviated SI.

10

Units of Measurement• Throughout any natural science course we are going to deal

with numbers. Numbers by themselves are meaningless. That is why need to have some sort of reference or standard to compare to. International System of Units or SI units, is based on the metric system.

QuantityQuantity Base UnitBase Unit SymbolSymbol

LengthLength MeterMeter mm

MassMass Gram Gram (Kilogram)(Kilogram) g (kg)g (kg)

TimeTime SecondSecond ss

TemperatureTemperature KelvinKelvin kk

Amount of Amount of substancesubstance MoleMole molmol

Electric currentElectric current ampereampere AA

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Prefixes of the SI Units• Since the SI Units are based upon the metric system, we use

prefixes to change the quantity we are discussing about which use multiples of ten.

• Some standard prefixes are:

PrefixPrefix AbbreviatioAbbreviationn

MeaningMeaning

Mega-Mega- MM 101066

Kilo-Kilo- kk 101033

Deci-Deci- dd 1010-1-1

Centi-Centi- cc 1010-2-2

Milli-Milli- mm 1010-3-3

Micro-Micro- µµ 1010-6-6

Nano-Nano- nn 1010-9-9

Pico-Pico- pp 1010-12-12

Examples:Examples:

1 megabyte = 1 megabyte = 1,000,000 bytes1,000,000 bytes

1 microgram = 1 microgram = 0.000001 grams0.000001 grams

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The Metric System

An easy way to measure

The Metric System

- Decimal system

- Powers of 10

- 2 Parts : Prefix – how many multiples of 10

milli, centi, Mega, micro

Base Unit - meter, liter, gram……

ex. Millimeter, centigram, kiloliter

Base Units

Length - meter ( m )

Mass - gram ( g )

Time - second ( s )

Temperature - Kelvin or ºCelsius ( K or C )

Energy - Joules ( J )

Volume - Liter ( L )

Amount of substance - mole ( mol )

PrefixesGiga 1 000 000 000 G 109

Mega 1 000 000 M 106

kilo 1 000 k 1000 = 103

hecto 1 00 h 100 = 102

deka 10 da 10 = 101

base 1 g, L, sec, m, etc. 1 = 100

deci 1/10 d .1 = 10-1

centi 1/100 c .01 = 10-2

milli 1/1 000 m .001 = 10-3

micro 1/1 000 000 μ 10-6

nano 1/1 000 000 000 n 10-9

pico 1/1 000 000 000 000 p 10-12

Converting• how far you have to move on a chart, tells you

how far, and which direction to move the decimal place.

• You need the base unit : (meters, Liters, grams,) etc.

• You need a chart!

• You need a plan!

Dr – uL Rule

21.5 g = __________mg 345.6 m = ___________ km21,500 0.3456

Down right up Left

Giga 1 000 000 000 G 109

Mega 1 000 000 M 106

kilo 1 000 k 1000 = 103

hecto 1 00 h 100 = 102

deka 10 da 10 = 101

BASE 1 g, L, sec, m, etc. 1 = 100

deci 1/10 d .1 = 10-1

centi 1/100 c .01 = 10-2

milli 1/1 000 m .001 = 10-3

micro 1/1 000 000 μ 10-6

nano 1/1 000 000 000 n 10-9

pico 1/1 000 000 000 000 p 10-12

Conversions

• Change 5.6 m to millimeters

k h D d c m

starts at the base unit and move three to the right.move the decimal point three to the right

56 00

Conversions

• convert 25 mg to grams• convert 0.45 km to mm• convert 35 mL to liters• It works because the math works, we are dividing

or multiplying by 10 the correct number of times

k h D d c m

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Accuracy and Precision

• When scientists make measurements, they evaluate both the accuracy and the precision of the measurements.

• Accuracy refers to how close a measured value is to an accepted value.

• Precision refers to how close a series of measurements are to one another.

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Accuracy and Precision

• Precision– A measurement of how well

several determinations of the quantity agree.

• Accuracy– The agreement of a measurement

with the accepted value of the quantity.

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Accuracy and Precision• An archery target illustrates the difference

between accuracy and precision.

SIGNIFICANT FIGURES

Significant Figures

Let’s take a look at some instruments used to measure

--Remember: the instrument limits how good your measurement is!!

Uncertainty in Measurements

Different measuring devices have different uses and different degrees of accuracy.

Significant figures (sig figs)

• We can only MEASURE at the lines on the measuring instrument

• We can (and do) always estimate between the smallest marks.

21 3 4 5in

4.5 inches

What was actually measured?

What was estimated?

4 inches

0.5 inches

21 3 4 5in

Significant figures (sig figs)

• The better marks… the better we can measure.

• Also, the closer we can estimate

21 3 4 5in

21 3 4 5in

21 3 4 5

4.55 inches

What was actually measured?

What was estimated?

in

4.5 inches

0.05 inches

So what does this all mean to you?

• Whenever you make a measurement, you should be doing three things……

1. Check to see what the smallest lines (increments) on the instrument represent

2. Measure as much as you can (to the smallest increment allowed by the device)

3. Estimate one decimal place further than you measured

Decimal Places Review

23456.789

thousandthshundredthstenths

onestenshundredsthousands

ten thousands

Your estimate MUST always be one (and only one) decimal place further to the right than your measurement

Practice

Your graduated cylinder can only accurately measure to tens of mL. To what decimal place should you estimate?

A balance can accurately measure to hundredths of grams. What decimal place will your estimate be?

Work Backwards NowWork Backwards Now

Look at the following measurements and determine the smallest increment that the measuring instrument could accurately measure to. Keep in mind that the last significant figure is the estimate.

100.3 g207 L1500 cm0.0004467 kg

ones

tens

thousandsOne-hundred thousandths

What is measured and what is estimated in the following measurements?

(Remember, significant figures include measured & estimated digits )

100.3

207

1500

0.0004467

4 Sig Figs ; Measured: 100. ; Estimated: 0.3

3 Sig Figs ; Measured: 2.0 X 102 ; Estimated: 7

2 Sig Figs ; Measured: 1000 ; Estimated: 500

4 Sig Figs ; Measured: 0.000446; Est: 0.0000007

SIGNIFICANT FIGURESThe RULES

Significant Figures

• The term significant figures refers to digits that were measured.

• When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

Significant Figures

1. All nonzero digits are significant.

2. Zeroes between two significant figures are themselves significant.

3. Zeroes at the beginning of a number are never significant.

4. Zeroes at the end of a number are significant if a decimal point is written in the number.

Significant FiguresWhat about the Zeros??

B M E

N A P

B

Beginning

M

Middle

E

End

N

Never

A

Always

P

Point

Significant Figures in Calculations

• When addition or subtraction is performed, answers are rounded to the least significant decimal place.

• When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.

Sig figs.

• How many sig figs in the following measurements?

• 458 g

• 4085 g

• 4850 g

• 0.0485 g

• 0.004085 g

• 40.004085 g

Sig. Fig. Calculations

Multiplication/Division• Rules:• The measurement w/ the smallest # of sig. figs

determines the # of sig. figs in answer

• Let’s Practice!!!• 6.221cm x 5.2cm = 32.3492 cm2 4 2 How many sig figs in final answer??? And the answer is…. 32 cm2

For example

27.93 6.4 =+

First line up the decimal places

+

Then do the adding

34.33

Find the estimated numbers in the problem

27.936.4

This answer must be rounded to the tenths place = 34.3

Practice• 4.8 + 6.8765=

• 520 + 94.98=

• 0.0045 + 2.113=

• 6.0 x 102 - 3.8 x 103 =

• 5.4 - 3.28=

• 6.7 - .542=

• 500 -126=

• 6.0 x 10-2 - 3.8 x 10-3=

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3

3

cm

gcm

Dimensional Analysis

• The “Factor-Label” Method– Units, or “labels” are canceled, or “factored” out

g

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• Steps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

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• Lining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

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• How many milliliters are in 1.00 quart of milk?

1.00 qt1.00 qt 1 L1 L

1.057 qt1.057 qt= 946 mL= 946 mL

qt mL

1000 mL1000 mL

1 L1 L

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• You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb1.5 lb 1 kg1 kg

2.2 lb2.2 lb= 35 cm= 35 cm33

1000 g1000 g

1 kg1 kg

1 cm1 cm33

19.3 g19.3 g

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• How many liters of water would fill a container that measures 75.0 in3?

75.0 in75.0 in33 (2.54 cm)(2.54 cm)33

(1 in)(1 in)33= 1.23 L= 1.23 L

in3 L

1 L1 L

1000 cm1000 cm33

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Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm8.0 cm 1 in1 in

2.54 cm2.54 cm= 3.2 in= 3.2 in

cm in

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

550 cm550 cm 1 in1 in

2.54 cm2.54 cm= 6.0 yd= 6.0 yd

cm yd

1 ft1 ft

12 in12 in

1 yd1 yd

3 ft3 ft

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

1.3 m1.3 m 100 cm100 cm

1 m1 m= 86 pieces= 86 pieces

cm pieces

1 piece1 piece

1.5 cm1.5 cm

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• Density is a ratio that compares the mass of an object to its volume.

Density

• The units for density are often grams per cubic centimeter (g/cm3 or g/mL).

• You can calculate density using this equation:

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• If a sample of aluminum has a mass of 13.5 g and a volume of 5.0 cm3, what is its density?

Density

• Insert the known quantities for mass and volume into the density equation.

• Density is a property that can be used to identify an unknown sample of matter. Every sample of pure aluminum has the same density.

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% Error

% error = O - A X 100

A

O = experimental value obtained (observed)

A = actual value (what you should get: text book)

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% Error

1.) What is the percent error in a lab if you find the reaction produces12.052 grams of calcium oxide. The text shows this reaction should produce 13.512 grams.

FINALLY!!!!!

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UNIT 3 MEASUREMENT