Unit 1.1: The Metric System and Unit Conversion

Vocabulary: Scientific notation: writing numbers as a decimal number between 1 and 10 followed by an integer power of 10 Significant figures: those digits in a number that carry meaning contributing to its precision Mass: the amount of matter contained in an object Weight: the force of gravity acting upon a mass Volume: the amount of space an object occupies Density: the ratio of the mass of an object to its volume Conversion factor: a ratio made from two measured quantities that are equal to each other; a conversion factor is a fraction that equals “one” Dimensional analysis: A method of analyzing/solving problems using the units of the measurements 2

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I.Scientific Notation (3.1) A.Useful for expressing very large or very small numbers: ex: 602,000,000,000,000,000,000,000 = 6.02 x ex: = 5.37 x B.In scientific notation, a number is written as the product of two numbers: y x 10 z 1.y is the “coefficient”: a number between 1 and 10 2.z is an integer exponent of 10 that indicates the number of decimal places moved to make this happen ex: 6.02 x o 6.02 is the coefficient, between 1 and 10 o Exponent is 23 (10 raised to a power) 4

C.Rules for writing numbers using scientific notation: 1.Place the decimal such that the resulting coefficient is between 1 and 10 2.Count the number of places you moved the decimal to determine the exponent: Remember: small numbers less than 1 will have a negative exponent while large numbers greater than 100 will have a positive exponent Another way to remember: if the decimal moves to the left, the exponent is positive, but if the decimal moves to the right, the exponent is negative 5

D.Example with a very small number: a.Place the decimal such that the resulting coefficient is between 1 and 10: 2.05 b.Count the number of places you moved the decimal to determine the exponent: 7 zeros and the 2 = 8 decimal places, so the exponent is -8 Remember: small numbers less than 1 will have a negative exponent while large numbers greater than 100 will have a positive exponent 2.So in scientific notation is 2.05 x Write in scientific notation: ____________ E.To 3 significant figures, write 8213 in scientific notation: __________________ (What are significant figures?!!) 6

II.Significant Figures (3.1) A.Include all verifiable digits in a number plus one unverifiable digit: How long is this nail? Longer than 6.3 cm, but less than 6.4 cm. You can approximate that it is about halfway, so 6.35 cm. 6.3 is verifiable and.05 is unverifiable, so 3 sig figs. 7

B.Rules for determining the number of sig figs: 1.All non-zero digits are significant. a.ex: in the number 95, there are two sig figs: 9 and 5 b.ex: in the number 12.34, there are four sig figs: 1, 2, 3, and 4 2.Zeros between any two non-zero digits are significant. a has four sig figs: 1, 0, 3, and 4 3.Trailing zeros in a number containing a decimal point are significant. a has 5 sig figs: 3, 4, 5, 0, and 0 b has 4 sig figs: 7, 8, 0, and 0 4.Leading zeros, however, are not significant. a has only two sig figs: 3 and 7; the zeros are simply placeholders. b.But, has four sig figs: 3,7, and the two zeros that follow the 7, but not the three zeros that hold the place… 8

C. Using sig figs. in calculations 1.A calculated answer cannot be more precise than the least precise measurement used in the calculation: a.4.3 cm x 5.2 cm = cm 2, but original measurements each only have 2 sig figs, so answer can only have 2 sig figs. So cm 2 becomes 22 cm 2. 1)Remember rules for rounding: less than 5 rounds down, 5 or greater rounds up. 9

2.Addition and Subtraction: answer should be rounded to same number of decimal places (not sig figs!) as the measurement with least number of decimal places. 10

3.Multiplication and Division: round answer to same number of sig figs as the measurement with least number of sig figs. 11

A.Based on multiples of 10, each with its own prefix 1.Memorize the most commonly used prefixes and the exponents associated with them: o kilo- (k): 10 3 (1 km = 1 x 10 3 m) o centi- (c): (1 cm = 1 x m) o milli- (m): (1 mm = 1 x m) o micro- (μ): (pronounced “mew”) o nano- (n): (1 nm = 1 x m) 12 III.The Metric System (SI) PrefixSymbolExponent Giga-G10 9 Mega-M10 6 Kilo-k10 3 Centi-c10 -2 Milli-m10 -3 Micro-μ10 -6 Nano-n10 -9

B.Five most common base units listed in table: 1.Serve as reference standards for comparing substances 2.Properties of matter that we will discuss: a.Mass: amount of matter in a substance b.Length: measures size/distance c.Volume: amount of space an object occupies d.Density: the ratio of an object’s mass to its volume e.Temperature: measures heat of an object f.Energy: capacity to do work 13 Physical QuantityName of UnitAbbreviation MassKilogramkg LengthMeterm TimeSeconds or sec TemperatureKelvinK Amount of substanceMolemol

a.Mass: the amount of matter contained in an object 1)Not quite the same as weight which is the force of gravity acting upon a mass. Mass is constant, but weight may change depending on gravity. 2)Base unit is the kilogram (kg) 3)1 L of 4°C = 1 kg; so 1 mL of water = 1 gram 14 mass

b.Length: measures size (or distance) 1)Base unit is the meter (m) 2)Large size/long distance measured in kilometers 1000 m = 1 km or 1 x 10 3 m 3)Small size/short distance measured in centimeters or millimeters 1 m = 100 cm o or 1 cm = 1 x m 1 m = 1000 mm o or 1 mm = 1 x m 15

c.Volume: measures the amount of space that an object occupies; is derived from length 1)Volume = length x width x height (V= l wh) 2)Because length, width, and height are all measures of size, volume is expressed in cubic meters (m 3 ) 3)But more commonly expressed in liters (L) Conversion is 1 cm 3 = 1 mL 16 1 sugar cube = 1 cm 3

d.Density: ratio of the mass of an object in relation to the volume it occupies; D=M/V Which is heavier: a pound of feathers or a pound of lead? 1.Density is expressed in g/L. 2.Density changes with temperature b/c the space a substance occupies changes with temperature but its mass is still constant: a.↑temp. = ↑ volume = ↓density b.↓ temp. = ↓ volume = ↑ density c.When something “condenses”, it takes up less space (↓ volume), becomes “more dense” 3.Less dense substances will float on more dense substances. 17

e.Temperature: measure of how hot or cold an object is 1)Heat always moves from a hotter object to a colder object (from more heat  less heat, like diffusion) 2)Almost all matter expands with increased temperature and contracts with decreased temperature. The very important exception is water! 3)Two equivalent units: a.Celsius (°C): water freezes at 0°C, boils at 100°C b.Kelvin (K): sets absolute zero at 0 K, equivalent to °C; 1)Kelvin scale – no degree symbol 2)Convert from K  °C as follows: K = °C °C = K

f.Energy: the capacity to do work or produce heat 1)Two common units: a)joule (J): the SI unit of energy b)calorie (cal): amount of heat needed to raise 1 g of pure water by 1°C c)Convert joules to calories as follows: 1 J = cal 1 cal = J 19

A.The same quantity can be expressed in many ways: 1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies 1 meter = 10 dm = 100 cm = mm = μm B.A ratio of two equal measurements will equal “1” 1.This ratio is called a “conversion factor” 2.Numerator is equivalent to denominator, but with different units IV.Unit Conversion 20 Conversion factors

C.Conversion factors do not change the value (because you are still multiplying by “1”) but it does change the unit of measurement. 1.Conversion factors have unlimited sig figs so they do not affect the rounding of an answer. D.Given any two equivalent units, you can create two different conversion factors: 1.Ex: 21

V.Dimensional AnalysisDimensional Analysis A way to analyze and solve problems using the units (dimensions) of the measurements A.List known quantities and unknown quantities B.Choose conversion factors that incorporate both known and unknown quantities. 1.Some problems may require more than one conversion C.Arrange conversion factors such that known quantities are in the denominator and unknown quantity is in the numerator. 1.This will allow you to cancel known units, leaving the correct units for the unknown quantity. 22

D.Dimensional Analysis (an example) How many seconds are there in 21 hours? 1.List known quantities and unknown quantities: a.Known: 21 hours 1 hour = 60 minutes (min) 1 minute = 60 seconds (s) b.Unknown: # of seconds in 21 hours 2.Choose conversion factor(s) that will leave unknown unit in the numerator: 23

3.Cancel out all units that appear in both the numerator and denominator, leaving only the unknown unit and solve: 24