Section 1.3Section 1.3MeasurementMeasurementPhysical SciencePages 14-20

ObjectivesObjectivesPerform calculations involving

scientific notation and conversion factors.

Identify the metric and SI units used in science and convert between common metric prefixes.

Compare and contrast accuracy and precision.

Relate the Celsius, Kelvin, and Fahrenheit temperature scales.

Using Scientific NotationUsing Scientific NotationWhen talking about astronomically large or

microscopically small numbers, it can become a hassle to count all the zeros you need to complete the number. Instead, you can use a shortcut called scientific notation.

Scientific notation is a way of expressing a value as the product of a number between 1 and 10 and a power of 10.◦ For example, a number like 300,000,000 would

be expressed as 3.0 x 108. The exponent (8) tells you that the decimal point is really 8 places to the right of the 3.

Using Scientific NotationUsing Scientific NotationFor numbers less than 1, the exponent

is negative.◦ For example, the number 0.00086 written

in scientific notation is 8.6 x 10-4. The negative exponent tells you how many decimal places there are to the left of the 8.6.

Scientific notation makes very large or very small numbers easier to work with.

Using Scientific NotationUsing Scientific NotationWhen multiplying numbers written in scientific

notation, you multiply the numbers that appear before the multiplication signs and add the exponents.◦ For example, when multiplying 1.2 x 105 m/s by 7.2 x

103 s, the answer you would get would be 8.64 x 108 s.

When dividing numbers written in scientific notation, you divide the numbers before the multiplication sign and subtract the exponents.◦ For example, when dividing 8.9 x 1011 m by 4.1 x 106

m/s, the answer you would get would be 2.17 x 105 s.

Sample ProblemSample ProblemA rectangular parking lot has a length of

1.1 x 103 meters and a width of 2.4 x 103 meters. What is the area of the parking lot?◦ Given: length (l) = 1.1 x 103 m,

width (w) = 2.4 x 103 m◦ Unknown: Area (A) = ?

A = l x w◦ Solve: A = (1.1 x 103 m) x (2.4 x 103 m)

A = (1.1 x 2.4) (103+3 ) (m x m)A = 2.6 x 106 m2

SI Units of MeasurementSI Units of MeasurementMeasurements do not make sense

unless they have a number and a unit.◦ Think about it – if I told you I’d give you

100 in 5, what would that mean? Dollars in minutes? Sentences in days?

Scientists use a set of measuring units called SI, or the International System of Units.◦ Its abbreviation comes from its original

French name, which was Système International d’Unites.

Base UnitsBase Units SI is built upon seven metric units, known as base

units. In SI, the base unit for length, or the straight-line

distance between two points, is the meter (m). The base unit for mass, or the quantity of matter in

an object or sample, is the kilogram (kg).Quantity Unit Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of substance mole mol

Electric current ampere A

Luminous intensity candela cd

Derived UnitsDerived Units Additional SI units, called derived units, are made from

combinations of base units. Two common examples are volume and density.

Volume is the amount of space taken up by an object. Density is the ratio of an object’s mass to its volume.

Quantity Unit Symbol

Area square meter m2

Volume cubic meter m3

Density kilograms per cubic meter kg/m3

Pressure pascal (kg/m·s2) Pa

Energy joule (kg·m2/s2) J

Frequency hertz (1/s) Hz

Electric charge coulomb (A·s) C

Metric PrefixesMetric PrefixesThe metric unit for a given quantity is not

always a convenient one to use, so we use prefixes to indicate how many times the number should be multiplied or divided by 10.

You can convert between units by moving the decimal place left or right according to the unit.

Here are some of the most common prefixes:

kilo hecto deka base deci centi milli

k h da d c m

1000 100 10 0.1 0.01 0.001

Conversion FactorsConversion FactorsThe easiest way to convert from one unit to

another is to use conversion factors.A conversion factor is a ratio of equivalent

measures that is used to convert a quantity expressed in one unit to another unit.

8848 meters x 1 kilometer

1000 meters

8.848 kilometers=

Limits of MeasurementLimits of MeasurementPrecision is a gauge of how exact a

measurement is.◦ For instance, using an analog clock is the

least precise, a digital clock is more precise, and a stopwatch would be the most precise.

The precision of a calculated answer is limited by the last precise measurement used in the calculation.

Accuracy is the closeness of a measurement to the actual value of what is being measured.

Measuring TemperatureMeasuring TemperatureA thermometer is an instrument that

measures temperature, or how hot an object is.There are three temperature scales that are

commonly used: Fahrenheit, Celsius, and Kelvin.◦ °C = 5/9(°F – 32.0°)◦ °F = 9/5(°C) + 32.0°◦ K = °C + 273

Here are the freezing point and melting point of water using the different scales:

Unit Freezing Point Melting Point

Fahrenheit 32°F 212°F

Celsius 0°C 100°C

Kelvin 273 K 373 K

VocabularyVocabularyScientific notationLengthMassVolumeDensityConversion factorPrecisionSignificant figuresAccuracyThermometer

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