Chapter 3: Scientific Measurement i.Math Review– ii.Uncertainty— significant figures & percent error iii.Units— SI units & metric system iv.Conversions

 Fractions  Decimal places expect you to  Exponents already know/  Graphing remember this!  Scientific notation  Algebra, solving for variables  Density = Mass / Volume; D=M/V Math Review Math- the “language” of Science

M x 10 n  M is the coefficient 1≤M<10  10 is the base  n is the exponent or power of 10 – Numbers less than 1, NEGATIVE exponent – Number greater than 10, POSITIVE exponent Scientific Notation

Standard not: Scientific not: 4.3x x10^-6 4.3E-6 Make sure you can put these into your calculator! Buttons to press: 4. 3 EXP or EE (-) 6 NOTE: Do NOT use the * sign when typing it into your calculator… Scientific Notation

Accuracy vs. Precision ACCURACY: indicates how close a measurement is to its true value. (comparison against a standard or control) PRECISION: indicates how close a series of measurements would be to each other…. E.g. a cm measurement is MORE PRECISE than a 3.0 cm measurement. *what is the variability associated with each measurement … ± 100? ±10? ±1? ± 0.1? ± ? More decimal places means greater precision.

Ex: Accuracy vs. Precision Whose measurements are more accurate when measuring a book that has a true length of cm? Whose are more precise? Susan: 17.0cm, 16.0cm, 18.0cm Amy: cm, 15.50cm, 15.52cm

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

How do we express the ACCURACY of a measurement? ERROR= experimental –accepted value % ERROR= |experimental –accepted| x100 accepted value

How do we express the PRECISION of a measurement/ instrument? SIGNIFICANT FIGURES (An answer to: To what decimal place should I make my measurement to?)

Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated. Go one extra decimal place than the last decimal place that is marked:  If every 100 is marked, measure to the 10’s  If every 10 is marked, measure to the 1’s  If every 1 is marked, measure to 0.1  If every 0.1 is marked, measure to 0.01

Ex: Reading Liquid Volumes Graduated Cylinder – Reading the Meniscus

VERSION #1 Rule #1: All non-zero digits are significant. Rule #2: Zeros in front of a number are not significant. Rule #3: Zeros between non-zero digits are significant. Rule #4: Zeros at the end of a number are significant if and only if there is a decimal point in the number. In scientific notation, only look at the COEFFICIENT Which numbers are sig figs in a given measurement?

VERSION #2 PACIFIC -Decimal PRESENT -Start from the left side at the first NONZERO #, Go to the end of the # ATLANTIC -Decimal ABSENT -Start from the right side at the first NONZERO #, Go to the end of the #

How many sig figs? x

Sig Figs in Addition/Subtraction The answer is rounded to the same DECIMAL PLACE as the number in the operation with the largest, last DECIMAL PLACE. Ex: 2.33 cm +3.0 cm 5.3 cm Sig Figs in Multiplication/Division The answer is rounded to the same number of SIG FIGS as the factor with the least number of SIG FIGS. Ex: 3.22 cm x 2.0 cm 6.4 cm 2

What has an INFINITE number of sig figs? EXACT numbers that are not measured, but are “by definition” Ex: 1 km = EXACTLY 1000 m (so 1000 m has an infinite number of sig figs) Counting numbers that are not measured. Ex: 3 apples

Base International System (SI) Units QuantityUnitSymbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of Substance molemol Luminous Intensity candelacd Electric Currentamperea

Some Derived SI Units QuantityunitSymbol Volumecubic meterm3m3 Densitykilograms per cubic meter kg/m 3 Speedmeter per secondm/s Newtonkg m/ s 2 N EnergyJoule (kg m 2 /s 2 )J PressurePascal (kg/(ms 2 )Pa

DENSITY DENSITY = MASS VOLUME Relates MASS and VOLUME Intensive physical property that will impact whether an object will sink or float in a liquid… (When people talk about something being “light” or “heavy”, they are usually commenting on density, not the actual weight or mass….)

Metric Prefixes NameSymbol giga-G10 9 mega-M10 6 kilo-k10 3 deci-d10 -1 centi-c10 -2 milli-m10 -3 micro-μ10 -6 nano-n10 -9 pico-p10 -12

Some Examples: VOLUME: m 3 cm 3 dm 3 L (Liter) mL 1 dm 3 = 1L 1cm 3 = 1mL WEIGHT: 1 Newton 1 N= kg m/s 2 ENERGY: Joule (J) calorie (cal) 1 cal= J 1 cal = quantity of heat needed to raise the temp of 1g of water by 1 o C. 1 Cal = 1kcal =1000cal

Temperature A measure of how hot or how cold an object is. SI Unit: kelvin ( K ) Note: not a degree Absolute Zero= 0 K K= o C o F= (1.8 o C ) is from ( )/ (100 – 0) = 180/100

Temperature Scales

Examples of conversions: 1.Convert 5km to m: NEW UNIT 5km x 1,000m =5,000m 1 km OLD UNIT 2.Convert 7,000m to km: 7,000m x 1 km = 7 km 1,000m 3.Convert 2.45cs to s: 2.45cs x 1 s = s 100cs

Example of converting a DERIVED unit Convert km/h to m/s : km x 1000 m x 1 h___ = 15.28m/s h 1 km 3600 s

One more EQUIVALENCY…. Remember, when we mentioned “AVOGADRO”? (not in Chapter 3, but so important!!!!) A small introduction to the Mole

Pair = 2 Dozen = 12

Avogadro Call me

1 mole = 6.02 x Avogadro’s Number (N A ) 6.02 x 10 23

Avogadro’s number a measured number that we now use for every substance, originally…. the number of Carbon-12 atoms in exactly grams of Carbon-12

1 pair = 2 1 dozen = 12 1 mole = 6.02 x 10 23

Element have different masses – “some atoms are big & heavy; some atoms are small & light” The mass of one mole (6.02 x ) of element’s atoms IN GRAMS can be found on the periodic table (a measured number with significant figures) Atomic Mass (Molar Mass) H Na

1 mole of Cu = 1 mole of Fe = 1 mole of H = 1 mole of H 2 = 1 mole of H 2 O = CONVERSION: 5.3 moles of Fe = ? g of Fe 2.5 g of H 2 O = ? Moles of H 2 O What is the mass of each of these?