Unit 2: Units and Measurements

Vocabulary 1British systemMetric systemSI systemkelvinderived unitsnatural unitsbase unitsecondmeterkilogramliterdensity

Units• Le Système International d'Unités, or the International System of Units--more commonly known as the SI system is an internationally agreed upon system of ____________.

• A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is ______________ of other units.

All measurements consist of two parts: a scalar (__________) quantity and the unit designation. In the measurement 8.5 m, the scalar quantity is 8.5 and the ____designation is meters.

A number indication “how much” and a unit indicates “of what”.

Nine fundamental units make up the SI system:Temperature (K) kelvin Length (m) meterTime (s) secondMass (kg) kilogramAmount of a substance (mol) moleElectric current (A) amphere Light intensity (cd) candelaplane angles (rad) radiansolid angles (sr) steradian

mm

gg

LL

ss

hhkkMM dd cc mm µµdada

101066 101033 101022 101011 1010-1-1 1010-2-2 1010-3-31010-6-6

T-Scale

Prefix Abbreviation Multiplicative Amount * The letter μ is the Greek letter lowercase equivalent to an m and is called “mu” (pronounced “myoo”).Prefix Symbol Factor Sci Notation Examplegiga G 1,000,000,000 10E9 gigameter (Gm)

mega M 1,000,000 10E6 megagram (Mg)

kilo k 1,000 10E3 kilometer (km)

deci d 1/10 10E-1 deciliter (dL)

centi c 1/100 10E-2 centimeter (cm)

milli m 1/1000 10E-3 milligram (mg)

micro µ 1/1000000 10E-6 microgram (µg)

nano n 1/1000000000 10E-9 nanometer (nm)

pico p 1/1000000000000 10E-12 picometer (pm)

32˚Fahrenheit 0 ˚ C 273.15 Kelvin

• The SI base unit of time is the _______ (s), based on the frequency of radiation given off by a cesium-133 atom.

• The SI base unit for ______is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second.

The meter is a little longer than a yard.

• The SI base unit of mass is the kilogram (kg), about __________.

• The SI base unit of temperature is the ______(K).

• Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as __________.

• Two other temperature scales are Celsius and Fahrenheit.

• Many physical phenomena are measured in units that are derived from SI units.

• A unit that is defined by a combination of base units is called a ________.

• ________ is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).

• Density is a derived unit, ______, the amount of mass per unit volume.

• Density is a measure of how much matter packed into a certain space.

• The density equation is _____________.

Vocabulary 2

significant figuresscientific notationpowers of tenrounding numbers dimensional analysisconversion factor

Significant Figures

• Often, precision is limited by the tools available.

• Significant figures include all known digits plus one _____________ .

Rules for Significant Figures–Rule 1: Nonzero numbers are always significant.–Rule 2: Zeros between nonzero numbers are always significant.–Rule 3: All final zeros to the right of the decimal are significant.–Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation.–Rule 5: Counting numbers and defined constants have an ________ number of significant figures.

The Atlantic-Pacific Rule:

"If a decimal point is Present, ignore zeros on the Pacific (left) side. If the decimal point is Absent, ignore zeros on the Atlantic (right) side. Everything else is significant."

If you're not in the Americas, you may prefer the following less colorful way to say the same thing:

1. Ignore leading zeros.

2. Ignore trailing zeros, unless they come after a decimal point.

3. Everything else is significant.

Example Question: How many significant figures are in the following numbers?

a. 0.000010 Lb. 907.0 kmc. 2.4050 x 10E-4 kgd. 300,100,000 g

Hint: If a decimal point is included, count the zeros. If there is no decimal point, the zeros do not count. Do not start counting until the first nonzero digit is reached as viewed from left to right.

• Scientific notation can be used to express any number as a number between 1 and 10 (the ________) multiplied by 10 raised to a power (the ________).

• Count the number of places the decimal point must be moved to give a coefficient between 1 and 10.

• The number of places moved equals the value of the exponent.

• The exponent is _______ when the decimal moves to the left and negative when the decimal moves to the right.

800 = 8.0 10__

0.0000343 = 3.43 ____• How many sig figs are in the numbers

listed above?

Addition and subtraction Involving measured Values

–Exponents must be ____ ______.–Rewrite values with the same exponent.–Add or subtract coefficients.

Example Questions (answers in scientific notation):a. 5.10 x 1020 + 4.11 x 1021b. 6.20 x 108 - 3.0 x 106c. 2.303 x 105 - 2.30 x 103d. 1.20 x 10-4 + 4.7 x 10-5e. 6.20 x 10-6 + 5.30 x 10-5f. 8.200 x 102 - 2.0 x 10-1

Multiplication and division– To multiply, multiply the coefficients,

then _____ the exponents.– To divide, divide the coefficients, then

_________ the exponent of the divisor from the exponent of the dividend.

Example Problems:

a. (3 x 107 km) x (3 x 107 km)b. (2 x 10-4 mm) x (2 x 10-4 mm)c. (90 x 1014 kg) ÷ (9 x 1012 L)d. (12 x 10-4 m ) ÷ (3 x 10-4 s)

Rounding Numbers•________ are not aware of significant figures.

•Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

Rules for rounding– Rule 1: If the digit to the right of the last

significant figure is less than 5, do not change the last significant figure.

– Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure.

– Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure.

– Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up.

Round each number to five significant figures. Write your answers in scientific notation.a. 0.000249950b. 907.0759c. 24,501,759d. 300,100,500

• Addition and subtraction– Round numbers so all numbers have the same

number of digits to the _______________.• Multiplication and division

– Round the answer to the same number of significant figures as the original measurement with the ________ significant figures.

Example Questions:

Complete the following calculations. Round off your answers as needed.a. 52.6 g + 309.1 g + 77.214 gb. 927.37 mL - 231.458 mLc. 245.01 km x 2.1 kmd. 529.31 m ÷ 0.9000 s

• Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another.

• A ____________ is a ratio of equivalent values having different units.

• A conversion factor is always equal to 1. Multiplying a quantity by a conversion factor does not change its value-because it is the same as multiplying by 1-but the units of the quantity can change.

Writing conversion factors–_____________ are derived from equality relationships, such as 1 dozen eggs = 12 eggs.–Percentages can also be used as conversion factors. They relate the number of parts of one component to 100 total parts.–A conversion factor must ________ one unit and introduce a new one.

Vocabulary 3accuracyprecisionerrorpercent errorgraphs

• _____________ refers to how close a measured value is to an accepted value.

• _____________ refers to how close a series of measurements are to one another.

Both Good Precision Poor Precision Good Precision

and Good Accuracy but Good Accuracy Poor Accuracy

x x x x x x x

x

x x x

x x x x x x x x

• _______ is defined as the difference between and experimental value and an accepted value.

• a- most precise• b- most accurate

• The ________equation is: error = experimental value – accepted value.

• Percent error expresses error as a percentage of the accepted value.

• When you calculate percent error, ignore any plus or minus signs because only the size of the error counts.

• A graph is a _____ display of data that makes trends easier to see than in a table.

• A circle graph, or pie chart, has wedges that visually represent ________ of a fixed whole.

• Bar graphs are often used to show how a quantity varies across categories.

• On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the _______.

• If a line through the points is straight, the relationship is linear and can be analyzed further by examining the _________.

• Interpolation is reading and estimating values falling between points on the graph.

• Extrapolation is estimating values outside the points by _________________.

This graph shows important ________ measurements and helps the viewer visualize a trend from two different time periods.