Measurement & Significant Figures Mrs. Page 2014-2015

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 balls 4 pizzas Exact relationships such as conversion factors 1 foot = 12 inches 1 meter = 100 cm Constants/ By Definition Pi, 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. counting 3. definition B. Measured numbers are obtained by

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 Units Measuring Base Unit Symbol Mass Kilogram kg Volume (solid) (liquid) Cubic centimeter Liter cm3 L Length Meter m Time Second s Temperature Kelvin K Amount of Substance Moles mol Force Newton N

Important Prefixes Prefix 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

What is the measure? What is the length of the wooden stick? 1) 4.5 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 Error Meniscus

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 23,456 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.