Metric SystemMetric System

Scientific NotationScientific Notation

Scientific notation is a way of writing very large Scientific notation is a way of writing very large and very small numbers more conveniently. and very small numbers more conveniently.

A number written in scientific notation has two A number written in scientific notation has two distinct parts:distinct parts:

1. A number with a decimal point that falls between 1 & 101. A number with a decimal point that falls between 1 & 10

2. The power of ten (either positive or negative) that shows 2. The power of ten (either positive or negative) that shows which way and how many places to move the decimal which way and how many places to move the decimal point to take the number out of scientific notation. point to take the number out of scientific notation.

Scientific NotationScientific Notation

The speed of light is 300,000,000 m/s. The speed of light is 300,000,000 m/s. Write this in scientific notation:Write this in scientific notation: 3.0 x 103.0 x 1088 m/s m/s

A snail has a speed of 0.00086 m/s. Write A snail has a speed of 0.00086 m/s. Write this in scientific notation:this in scientific notation: 8.6 x 108.6 x 10-4-4

Scientific NotationScientific Notation

Multiplying – multiply the numbers that Multiplying – multiply the numbers that appear before the multiplication signs and appear before the multiplication signs and add the exponentsadd the exponents (3.0 x 10(3.0 x 1088)(5.0 x 10)(5.0 x 1022) = 15 x 10) = 15 x 101010 = 1.5 x 10 = 1.5 x 101111

Division – divide the numbers that appear Division – divide the numbers that appear before the exponential terms and subtract before the exponential terms and subtract the exponentsthe exponents (1.5 x 10(1.5 x 101111)/(3.0 x 10)/(3.0 x 1088) = .50 x 10) = .50 x 1033 = 5.0 x 10 = 5.0 x 1022

Standards of MeasurementStandards of Measurement

A standard is an exact quantity that people A standard is an exact quantity that people agree to use for comparison or measurement.agree to use for comparison or measurement.

The first such system of measurement called The first such system of measurement called the Metric System was devised by a group of the Metric System was devised by a group of scientists in the late 1700’s.scientists in the late 1700’s.

In 1960 an improved version of the Metric In 1960 an improved version of the Metric System was devised and is now called the System was devised and is now called the International System of Units. (SI)International System of Units. (SI)

The Seven Fundamental Units of The Seven Fundamental Units of MeasurementMeasurement

MeasurementMeasurement SI UnitSI Unit

LengthLength meter (m)meter (m)

MassMass kilogram (kg)kilogram (kg)

VolumeVolume liter (L)liter (L)

TimeTime second (s)second (s)

TemperatureTemperature Kelvin (K)Kelvin (K)

Amount of SubstanceAmount of Substance mole (mol)mole (mol)

Electric CurrentElectric Current Ampere (A)Ampere (A)

Commonly Used PrefixesCommonly Used Prefixes

PrefixPrefix SymbolSymbol MeaningMeaning Numeric Numeric FormForm

FractionFraction

Kilo -Kilo - kk ThousandThousand 1,0001,000 1,0001,000

Hecto -Hecto - hh HundredHundred 100100 100100

Deca -Deca - dada TenTen 1010 1010

(base unit)(base unit) m, L, gm, L, g OneOne 11 11

Deci -Deci - dd TenthTenth 0.10.1 1/101/10

Centi - Centi - cc HundredthHundredth 0.010.01 1/1001/100

Milli -Milli - mm ThousandthThousandth 0.0010.001 1/1,0001/1,000

MeasurementMeasurement

PrecisionPrecision – A gauge of how EXACT a – A gauge of how EXACT a measurement is measurement is

Ex: a digital clock is more precise than a Ex: a digital clock is more precise than a regular clockregular clock

MeasurementMeasurement

AccuracyAccuracy – the closeness of a measurement – the closeness of a measurement to the accepted value for a quantity.to the accepted value for a quantity.

Ex: an atomic clock is more accurate than Ex: an atomic clock is more accurate than our school clocksour school clocks

MeasurementMeasurement

Measurements can be accurate but not Measurements can be accurate but not precise.precise.

They can be precise but not accurate.They can be precise but not accurate. They can be both accurate and precise.They can be both accurate and precise. They can be neither accurate nor precise.They can be neither accurate nor precise.

Measuring LengthMeasuring Length

When measuring length, we When measuring length, we will be using a metric ruler or will be using a metric ruler or meterstick.meterstick.

The numbered divisions are 1 The numbered divisions are 1 cm divisions.cm divisions.

The smallest divisions marked The smallest divisions marked are 1 mm divisions. are 1 mm divisions.

Measuring MassMeasuring Mass

When using an electronic balance, write When using an electronic balance, write down all numbers printed on the screen. down all numbers printed on the screen.

When using a triple beam balance, the When using a triple beam balance, the mass can be measured accurately to 0.01 mass can be measured accurately to 0.01 grams.grams.

Measuring VolumeMeasuring Volume

The amount of space occupied by an The amount of space occupied by an object is called its volume.object is called its volume.

There is no specific way to measure the There is no specific way to measure the object’s volume. object’s volume.

Measuring the Volume of a Measuring the Volume of a SolidSolid

When measuring the volume of a solid When measuring the volume of a solid object, multiply its length x width x height.object, multiply its length x width x height.

Typically the volume of a solid is Typically the volume of a solid is measured in either cubic centimeters (cmmeasured in either cubic centimeters (cm33) ) or cubic meters (mor cubic meters (m33).).

Measuring the Volume of a LiquidMeasuring the Volume of a Liquid

When measuring a liquid volume, When measuring a liquid volume, one must choose the appropriate one must choose the appropriate device based upon the amount of device based upon the amount of liquid to be measured.liquid to be measured.

For smaller amounts of liquid, a For smaller amounts of liquid, a graduated cylinder is used.graduated cylinder is used.

For larger amounts of liquids, a For larger amounts of liquids, a beaker would be used. beaker would be used.

The most common units used for The most common units used for these types of volumes are liters these types of volumes are liters (L) and milliliters (mL).(L) and milliliters (mL).

DensityDensity

Density is an important characteristic Density is an important characteristic property of matter.property of matter.

When one speaks of lead as being “heavy” When one speaks of lead as being “heavy” or aluminum as “light,” one is actually or aluminum as “light,” one is actually referring to the density of these metals.referring to the density of these metals.

Density is defined as mass per unit Density is defined as mass per unit volume.volume.

Calculating DensityCalculating Density

An object with a mass of 10 grams and a An object with a mass of 10 grams and a volume of 5 cmvolume of 5 cm33 has a density of 2 g/cm has a density of 2 g/cm33..

10 g10 g = 2g/cm = 2g/cm33

5 cm5 cm33

V

mD

volume

massDensity

Comparing DensitiesComparing Densities

•Where is Where is the most the most dense dense object?object?

•Where is Where is the least the least dense dense object?object?

Factor Label MethodFactor Label Method

Not all objects that are measured are in the Not all objects that are measured are in the units that are needed.units that are needed.

The factor label method is a The factor label method is a mathematical way to convert from mathematical way to convert from the units you have to the units you the units you have to the units you need.need.

In order to eliminate the unwanted units, you In order to eliminate the unwanted units, you design a ladder-type set up of equalities that design a ladder-type set up of equalities that cancel out the units you no longer want.cancel out the units you no longer want.

Steps of Factor LabelSteps of Factor Label

Example: How many liters are there in 3650 mL?Example: How many liters are there in 3650 mL?

1. Find an equality relating to the original units and 1. Find an equality relating to the original units and write it down in the ladder set up. Make sure to write it down in the ladder set up. Make sure to put the units that you DO NOT want in the put the units that you DO NOT want in the denominator. Cross out the units that match.denominator. Cross out the units that match.

3650 mL3650 mL x x 1 L1 L________ = _______ L= _______ L

1000 mL1000 mL

Steps of Factor LabelSteps of Factor Label

2. Ask yourself if you want the units in the numerator. If 2. Ask yourself if you want the units in the numerator. If you don’t, repeat steps 1 and 2 until you get the correct you don’t, repeat steps 1 and 2 until you get the correct units in the numerator.units in the numerator.

3. Solve the problem by multiplying the numbers in the 3. Solve the problem by multiplying the numbers in the numerator, then dividing by the numbers in the numerator, then dividing by the numbers in the denominator.denominator.

3650 mL x3650 mL x 1 L_____1 L_____ = 3.65 L= 3.65 L

1000 mL1000 mL