Chapter 2 Standards of Measurement Objectives:  Understand Mass and Weight (2.1)  Identify the metric units of measurement (2.6)  Explain what causes.

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Chapter 2 Standards of Measurement Objectives:  Understand Mass and Weight (2.1)  Identify the metric units of measurement (2.6)  Explain what causes uncertainty in measurements (2.7, 2.8 – 2.12)  Learn how to use significant digits and scientific notation (2.2 – 2.5)  Dimensional Analysis (2.8)  Density (2.12)

The Metric System (2.6) The International System of Units Standards of measurement Base units (7) – see Table 2.2 (pg 20) 1.MASS: 2.LENGTH: 3.TIME: 4.COUNT, QUANTITY: 5.TEMPERATURE: 6.ELECTRIC CURRENT: 7.LUMINOUS INSTENSITY:

The Metric System Derived Units:  AREA:  VOLUME:  ENERGY:  FORCE:  PRESSURE:  POWER:  VOLTAGE:  FREQUENCY:  ELECTRIC CHARGE:

The Metric System Metric Prefixes – make base unit larger or smaller Table 2.1 – must know bolded prefixes Based on 10 Math method vs. “Stairs”

Convert a volume of 12 microliters into centiliters Express a distance of 15 meters in kilometers Convert 83 cm into meters Which is the longer amount of time, 1351 ps or 1.2 ns? Convert 16 dL into L Conversion Practice

Uncertainty in Measurement Why are digits in measurements uncertain? 1.Instruments never 2.Always involves estimation  Choose the right instrument for the job  May be estimated for you (electronic scales)  Scale is marked but you estimate the in- between

Uncertainty in Measurement Precision:Accuracy:

Significant Digits All digits known with certainty plus one final digit which is uncertain (or estimated) All non-zeros are significant (143.34) A zero is significant when : –It is between –It is at the A zero is not significant when: –It is before –It is at the

Significant Digits - PRACTICE How many significant digits? 1. 54.23 2. 23.00005 3. 0.0004 4. 35000 5. 0.000504 6. 45.623200 7. 5,000,000 8. 4,000,000.1

Significant Digits - Calculations Addition and Subtraction –Round answer to have final digit in the SAME PLACE as the last digit in the LEAST ACCURATE MEASUREMENT 1.21 + 5.002 + 10. = 16.212 becomes 16 34.5 + 12.45 + 23.0505 = 186.31 + 11.1 = 12.0231 + 3.86 = 0.100012 + 120. = 1200 + 12 + 15 + 0.5 = 1200 + 12 + 15 + 0.5 =

Significant Digits - Calculations Multiplication and Division –The answer has as many sig figs as the number with the fewest sig figs 14.8 x 3.1 = 45.88 becomes 46 18.2 x 3.0 = 52/1.5 = 321.868783 x 1 = 2400 x 2.123 = 15000/12.354 =

Scientific Notation Convenient way of writing very large or very small numbers and showing Number between 1 & 10 with a 5120 becomes Move decimal point in original number to make Move left = ; move right =

Scientific Notation Practice 123,000 = 0.000045 = 23.45 = 0.0000000003 = 1,000,000 =

Scientific Notation Adding and subtracting –Numbers must be the SAME POWER –1.4 x 10 4 + 2.1 x 10 5 (must change to 21.0 x 10 4 ) and then = 2.24 x 10 4 –3.2 x 10 3 + 1.8 x 10 2 =

Scientific Notation Multiplying –Add exponents –(2.0 x 10 3 ) x (3.0 x 10 4 ) = Dividing –Subtract exponents –(8.2 x 10 8 ) x (4.1 x 10 4 ) =

Types of Measurements Mass – amount of matter in a body – – Weight – measure of earth’s gravitational attraction for that object – –

Types of Measurements Volume – –Cubic meter or –Many instruments to measure Temperature – –Kelvin –Degrees

Conversion Factors Enable movement between metric system and “English” system See back cover of book and Appendix III Common conversions you should memorize –1 inch = 2.54 cm –1 mile = 1.609 km –1 kg = 2.20 pounds –1 mL = 1 cm 3 –0 K = -273.15 0 C – 0 F = 1.8( 0 C) + 32

Dimensional Analysis (Problem Solving) Remember: ALWAYS use UNITS OF MEASUREMENT in your work!!! A technique of converting between units –Same system (metrics) –Different systems (inches to meters) –Chemical equations….later chapters…

Dimensional Analysis (Problem Solving) Conversion Factors: ratio derived from the equality between 2 different units 3 feet = 1 1 dollar = 1 1 yard4 quarters 1 yard4 quarters CF can be written either way 1 minute = 1 60 seconds = 1 1 minute = 1 60 seconds = 1 60 seconds 1 minute

Dimensional Analysis (Problem Solving) The “t” method unit given unit wanted = unit wanted unit given Example: How many liters are in 125.6 gallons? 125.6 gallons3.785 Liters = 1 gallon Conversion Factor 475.4 L

4.15 hours 60 minutes60 seconds = 1 hour 1 minute 1.5 mL 1 L 1 gal 4 qts 4 cups = 1000 mL 3.785 L 1 gal 1 qt How many seconds are in 4.15 hours? Dimensional Analysis (Problem Solving) If a student needs 1.5 mL of water, how many cups does he need? 14900 s 0.0063 cups

Density Common ratio used in chemistry Physical property of a substance Mass/volume D = m v SI units: kg/m 3 Solid –g/cm 3Liquid –g/mLGas –g/L Can change due to temperature and/or pressure changes

m = d x v = 0.24 g/cm 3 x 2 cm 3 = Density 1.Find the density of a piece of metal with a volume of 2.7 cm 3 and a mass of 10.8 g. D = m v = 10.8 g 2.7 cm 3 = 4.0 g/cm 3 2. Determine the mass of an object with a density of 0.24 g/cm 3 and a volume of 2 cm 3. SIG FIGS!!! 0.5 g 0.48

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