Measurement & Significant Figures

Measurement & Significant

Figures

Mrs. Page2014-2015

By the end of this lesson you should be able to:

• Distinguish between exact and measured numbers.

• Identify different pieces of lab equipment, what it measures & the units of measurement

• State the SI units for mass, length, volume, temperature, and amount of a substance.

• Use a ruler, graduated cylinder, triple beam balance to make accurate measurement (to correct place value)

By the end of this lesson you should be able to:

• Explain how a measured number tells the audience about the accuracy of the tool used to make a measurement

• Determine the number of significant figures in a given number

• Perform calculations & express solutions with correct number of significant figures

2 Types of Numbers– Exact– Measured

Exact Numbers (3 types)Counting objects are always exact

2 soccer balls4 pizzas

Exact relationships such as conversion factors1 foot = 12 inches1 meter = 100 cm

Constants/ By DefinitionPi, Avogadro’s #, speed of light

Measured Numbers• Measured numbers will always include

some degree of ERROR• An instrument is used for measuring and

therefore the user must at some point estimate the value.

• When you use your calculator to calculate using a measured number your answer can only be as accurate as your worst measurement.

Learning Check

A. Exact numbers are obtained by 1. using a measuring tool

2. counting3. definition

B. Measured numbers are obtained by 1. using a measuring tool

2. counting3. definition

Learning Check

Classify each of the following as an exact or a

measured number.

1 yard = 3 feet

The diameter of a red blood cell is 6 x 10-4 cm.

There are 6 hats on the shelf.

Gold melts at 1064°C.

Metric System• Every measurement has 2 parts:

– Number– Unit (scale)

• SI System (le Systeme International) is based on the metric system

• Prefix + Base Unit • Prefix tells you the power of 10 to multiply

by (easy for conversions)

SI UnitsMeasuring Base Unit Symb

olMass Kilogram kgVolume (solid) (liquid)

Cubic centimeterLiter

cm3L

Length Meter mTime Second sTemperature Kelvin KAmount of Substance Moles molForce Newton N

Important PrefixesPrefix Symbol Amount Scientific

Notation

Giga - G 1,000,000,000 109

Mega - M 1,000,000 106

Kilo - k 1,000 103

Deci d 0.1 10-1

Centi - c 0.01 10-2

Milli - m 0.001 10-3

Micro - µ 0.000001 10-6

Nano- n 0.000000001 10-9

Dimensional Analysis

• Coming to a lesson soon

Tool: Ruler• Measures length• Measures in centimeter (cm)

• All measurements have a degree of uncertainty!• We can see the markings between 1.6-1.7cm• We can’t see the markings between the 0.6-0.7• We must “guess” between 0.6 & 0.7• We record 1.67 cm as our measurement• The last digit an 7 was our guess...stop there

1 2 3 4 cm

What is the measure?

What is the length of the wooden stick?1) 4.5 cm 2) 4.54 cm 3) 4.547 cm

What is the measure in cm?

Beaker• Measures Volume• This tool measures in

milliliters (mL)• Not very accurate

(what is the interval?)

Conical (Erlenmeyer) Flask

• Measures volume• Units – mL• Used when

heating to avoid splashing and/or to collect gasses

• Accurate???

Graduated Cylinder

• Measures Volume• Units – mL• Accurate???

Reading a Graduated Cylinder

Avoid Parallax ErrorMeniscus

• What is the level of uncertainty?

• To what place value should we record an answer?

• MUST look at INTERVAL

• 17.6mL

Reading a Graduated Cylinder

Which Gives the MOST Accurate Measure? Why?

Triple Beam Balance

• Measures Mass• This tool

measures in grams (g)

Reading a Balance

Electronic Scale

• Measures mass in grams (g)

• Digital equipment– Note all digits recorded– Uncertainty should be

on equipment– Often must be

calibrated

BRAIN BREAK

• http://brainbreaks.blogspot.com/2009/03/figure-eight-brain-break.html

Significant Figures

• Numbers that are important for performing calculations to ensure that your final answers are accurate

• There are many significant figure rules

THE RULES

• All non-zero numbers are significant• Examples:

– 65.23 • 4 sig. figs.

– 23,456• 5 sig. figs.

– 1.234567 • 7 sig. figs

THE RULES

• All zeros between two non-zero numbers are significant

• Examples:– 2014

• 4 sig. figs

– 300,002• 6 sig. figs

– 1.0005• 5 sig. figs.

THE RULES

• Place holder zeros are NOT significant – Leading zero - before any digits

• 0.0012 – 2 sig. figs

– Trailing zeros – after digits but BEFORE a decimal • 345,000

– 3 sig. figs

• 41,980,000.– 4 sig. figs

THE RULES

• All zeros at the end of a number and AFTER the decimal point are significant

• Examples:– 5.0000

• 5 sig figs

– 402.0• 4 sig figs

– 0.450• 3 sig figs

THE RULES

• Significance of a DECIMAL point• MUST PAY ATTENTION• Try some more as Mrs. Page puts them on

the board.• QUESTION???? ASK NOW!!!!

Calculations w/ Sig. Figs.RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers. (answer has # of sig. figs of smaller # of sig figs)

Calculations w/ Sig. Figs.RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers.