Units of Measuremen

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•Many properties of matter are quantitative, they are associated with numbers•Always specify units when expressing a measured quantity•The units used for scientific measurement are those of the metric system (base 10)•In 1960 an international agreement was reached specifying the Systeme International d’Unites (SI)•The SI system has seven base units from which all other units are derived•Prefixes are used to express different amounts of the units

The SI Base Units

Base Quantity Name Symbol

length meter m

Mass kilogram      

kg

Time second s

electric current ampere A

thermodynamic temperature       Kelvin K

amount of substance mole mol

luminous intensity candela cd

Metric Prefixes• Base SI units are

not always convenient to use

• Using big numbers, such as 10,000 meters can be a hassle

• This can be fixed by using metric prefixes

• 10,000 meters would become 10 kilometers (10 km)

Scientific Notation• To write a number in scientific notation:• Put the decimal after the first digit and drop the zeroes. • In the number 123,000,000,000 The coefficient will be 1.23 • To find the exponent count the number of places from where you put the

decimal to the end of the original number. • In 123,000,000,000 there are 11 places. Therefore we write

123,000,000,000 as:

1.23 x 1011

• For small numbers we use a similar approach. Numbers smaller than 1 will have a negative exponent. A millionth of a second is:

• 0.000001 seconds or 1.0 x 10-6 • http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl

Precision & Accuracy

• Precision is a measure of how closely individual measurements agree with one another

• Accuracy refers to how closely individual measurements agree with the correct or “true” value

• In general, the more precise the measurement, the more accurate it is

• We gain confidence in accuracy if we obtain nearly the same value in many different experiments

• It is possible for a precise value to be inaccurate

length And Mass

• Length is a measure of the distance from one point to another

• The SI unit for length is the meter (m) and is slightly longer than a yard

• One meter = the distance light travels in a vacuum in 1/299,792,458th’s of a second

• Mass is a measure of the amount of matter in an object

• The SI unit for mass is the kilogram (kg) which about equal to 2.2 pounds

• Mass and weight are not the same!!!...weight is the force that the mass exerts due to gravity…you can be weightless, but you cannot be mass-less…you have the same mass in space as you do on Earth

• What are some tools to measure mass and length?

Derived Units

• The SI base units are combined to derive, or make, other units of other quantities

• Other SI units can be formed from combinations of base units…called Derived Units

• Both the numbers and the units are calculated when finding a derived unit!!

• Area = length x width…5.0 m x 3.0 m = 15 (m x m) or 15 m2

area square meter m2

volume cubic meter m3

speed, velocity meter per second m/s

acceleration meter per second squared m/s2

wave number 1 per meter m-1

density, mass density kilogram per cubic meter kg/m3

specific volume cubic meter per kilogram m3/kg

current density ampere per square meter A/m2

magnetic field strength ampere per meter A/m

concentration(of amount of substance)

mole per cubic meter mol/m3

luminance candela per square meter cd/m2

refractive index (the number) one 1(a)

Volume• Volume is the amount

of space an object takes up

• The volume of a cube is given by its length cubed (length)3

• The SI unit for volume is the cubic meter, m3

• Since this unit is so large, in chemistry we often use the cubic centimeter instead cm3

• Volume of irrelgular objects can also be found by displacing it in a liquid…a process called displacement

• 1 milliliter (mL) is equal to one cubic centimeter

• 1 mL = 1cm3

Volume

• The metric unit for liquid volume is the liter (L)…L for liquid!!

• A milliliter (mL) is about the size of a drop

• A liter is about the size of a pitcher

• Always measure from the bottom of the meniscus

Density

• Density is mass per unit volume …how heavy something is compared to its size.

• It’s the amount of mass in a certain volume • Density does not depend on the amount of the

substance! • D = M / V; Density = mass / volume

Density Simulation

Time & Temperature

• The SI unit for time is the second (s)

• The Kelvin scale is the SI temperature scale. Its units are K

• The Celsius scale is widely used in chemistry…it was originally based on the assignment of 0 degrees to the freezing point of water and 100 degrees C for the boiling point of water

• 0 K is the lowest possible temperature -273.15 O C, or absolute zero…notice we do not use the degree sign in Kelvins (°)

K=°C + 273.15

Uncertainty in Measurement

• In science there are exact and inexact numbers (values with uncertainty)

• Exact values are defined…there are exactly 12 eggs in 1 dozen; 1000g in one kg

• Numbers obtained by measurement are always inexact…uncertainty always exists in measured quantities

• This is due to limitations of equipment, human errors

• When measuring length, the end of the stick or tape may cause errors

• Parallax occurs when your head is to the left or the right. Place the mark on the stick in contact with what is being measured

• For volume, take a measurement at the bottom of the meniscus

• Suppose you weigh a dime on a balance capable of measuring to the nearest 0.0001g. It may have a mass of 2.2405g + 0.0001g

• The + notation is used to express the uncertainty…but in scientific work it is understood and we don’t write it

Significant Figures

• 2.2405 has 5 significant figures

• The number of significant figures indicates the exactness of a measurement

Significant Figures Rules

• Nonzero digits are always significant (456 cm = 3 sig figs)• Zeros between nonzero digits are always significant (1005g = 4 sig figs• Zeros at the beginning of a number are never significant (0.002g = 1 sig)• Zeros that fall both at the end of a number and after the decimal point are

always significant (0.0200g = 3; 3.0 cm = 2)• When a number ends in zeros but contains no decimal point, the zeros may

or may not be significant (130cm = 2 or 3)…the use of scientific notation removes this ambiguity

Significant Figures in Calculations

• The precision of the result is limited by the precision of the measurements

• There are two rules (1) In multiplication and division, the result must be reported with the same number of significant figures as the measurement with the fewest significant figures…round off!!

• (2) In addition and subtraction the result cannot have more digits to the right of the decimal point than any of the original numbers