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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