COS 12.0

IDENTIFY METRIC UNITS FOR MASS, DISTANCE, TIME, TEMPERATURE,

VELOCITY, ACCELERATION, DENSITY, FORCE, ENERGY & POWER

WHAT YOU’LL LEARN• Name the prefixes used in SI & indicate what multiple of

ten each one represents.• Identify SI units and symbols for mass, length (distance),

time, temperature, velocity, acceleration, density, force, energy & power.

• Convert related SI units.• Use scientific notation & significant figures in problem

solving.• Identify the significant figures in calculations.• Understand the difference between precision & accuracy

UNITS OF MEASUREMENTUNITS OF MEASUREMENT

What is a measurement?• A measurement is a number and a unit.• 14.5 meters, 35 dozen, and 1 hour are all

measurements.

DEFINITIONS

DERIVED UNIT

• measurement unit using a combination of units

• g/cm3, m/s2, m/s, g/ml, kW

DISTANCE (LENGTH)

• measure of straight-line distance between two points

• meter, kilometer, mile

MASS

• measure of amount of matter in an object

TIME

• measured period during which an action, process, or condition exists or continues

• seconds, minutes, hours, days, years…

TEMPERATURE

• measure of average kinetic energy of all particles in an object

• Kelvin

• absolute zero (0 K)

• coldest possible temperature

• = -273°C

VELOCITY

• measures the speed & direction of a moving object

ACCELERATION

• rate of change of velocity, occurs if an object speeds up, changes direction or slows down

FORCE

• push or pull that one body exerts on another

ENERGY

• capacity to do work

POWER

• amount of work done or energy transferred

ELECTRIC CURRENT

• flow of electric charge through a wire or conductor

DENSITY

• mass per unit volume of a material

VOLUME

• amount of space occupied by an object

• unit is liter

• 1 ml = 1 cm3

WEIGHT

• measure of gravitational force exerted on an object

JOULE

• SI unit of energy measuring heat, electricity and mechanical work

WATT

• SI deried unit of power, equal to one joule of energy per second.

• measures a rate of energy use or production.

NEWTON

• SI derived unit of force

TABLE OF UNITS

Quantity Measured Unit Symbol

Mass Kilogram kg

Distance (length) Meter m

Time Second s

Temperature Kelvin K

Velocity m/s

Acceleration m/s2

Density kg/m3

Force Newtons N

Energy Joule J

Power Watt W

Electric current Ampere A

Volume Liter l

Bold letters indicate derived units

SIGNIFICANT FIGURES

SIGNIFICANT FIGURES

Significant figure • prescribed decimal place that determines the

amount of rounding off to be done based on the precision of the measurement

Precision • exactness of a measurementAccuracy • description of how close a measurement is to the

true value of the quantity measured

Accuracy and PrecisionChapter 1

Accuracy and PrecisionChapter 1

Rules For Significant Digits Digits from 1-9 are always significant. Zeros between two other significant

digits are always significant One or more additional zeros to the

right of both the decimal place and another significant digit are significant.

Zeros used solely for spacing the decimal point (placeholders) are not significant.

EXAMPLES OF SIGNIFICANT DIGITS

EXAMPLES # OF SIG. DIG. COMMENT

453 kg 3 All non-zero digits are always significant.

5057 L 4 Zeros between 2 sig. dig. are significant.

5.00 3 Additional zeros to the right of decimal and a

sig. dig. are significant.

0.007 1 Placeholders are not sig.

Multiplying and DividingMultiplying and Dividing • RULE: When multiplying or dividing, your answer may only RULE: When multiplying or dividing, your answer may only

show as many significant digits as the multiplied or divided show as many significant digits as the multiplied or divided measurement showing the measurement showing the leastleast number of significant digits. number of significant digits.

• Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm= 5946.50525 cm33

• We look to the original problem and check the number of We look to the original problem and check the number of significant digits in each of the original measurements: significant digits in each of the original measurements:

• 22.37 shows 4 significant digits. 22.37 shows 4 significant digits. • 3.10 shows 3 significant digits.3.10 shows 3 significant digits.• 85.75 shows 4 significant digits.85.75 shows 4 significant digits.• Our answer can only show 3 significant digits because that is Our answer can only show 3 significant digits because that is

the least number of significant digits in the original problem.the least number of significant digits in the original problem.• 5946.50525 shows 9 significant digits, we must round to the 5946.50525 shows 9 significant digits, we must round to the

tens place in order to show only 3 significant digits. Our final tens place in order to show only 3 significant digits. Our final answer becomes 5950 cmanswer becomes 5950 cm33. .

Adding and SubtractingAdding and Subtracting

• RULE: When adding or subtracting your answer can only RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having show as many decimal places as the measurement having the the fewestfewest number of decimal places. number of decimal places.

• Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 gExample: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g• We look to the original problem to see the number of We look to the original problem to see the number of

decimal places shown in each of the original decimal places shown in each of the original measurements. 2.1 shows the least number of decimal measurements. 2.1 shows the least number of decimal places. places.

• We must round our answer, 20.69, to one decimal place We must round our answer, 20.69, to one decimal place (the tenth place). (the tenth place).

• Our final answer is 20.7 g Our final answer is 20.7 g

SCIENTIFIC NOTATION

Scientific Notation• The number 123,000,000,000 in scientific notation is

written as : • 1.23 x 1011

• The first number 1.23 is called the coefficient. • It must be greater than or equal to 1 and less than 10. • The second number is called the base . • It must always be 10 in scientific notation. • The base number 10 is always written in exponent form. • In the number 1.23 x 1011 the number 11 is referred to as

the exponent or power of ten.

Scientific Notation

• To write a number in scientific notation:• Put decimal after first digit and drop zeroes. • 1.23000000000• In number 123,000,000,000 coefficient will be 1.23 • To find exponent count number of places from

decimal to the end of number. • In 123,000,000,000 there are 11 places.• Therefore we write 123,000,000,000 as: • 1.23 x 1011

Scientific Notation

• For small numbers we use a similar approach. • Numbers smaller than 1 will have a negative

exponent. • A millionth of a second (.000001) is:• 1.0 x 10-6

Standard Form• Is just opposite of scientific notation!• 6.33 X 108 =• 633,000,000• All we’ve done is moved decimal eight (8) places to

right. • 5.18 X 10-7 =• .000000518• All we’ve done is moved decimal seven (7) places to left.• IT’S THAT EASY!

Write the following in scientific notation:

• 4,100,000 = _______________• 345,600,000,000 = _________• 0.0456= ________________• 0.00000012=____________• 0.00305= ____________

4.1 x 106

3.456 x 1011

4.56 x 10-2

1.2 x 10-7

3.05 x 10-3

Write the following in standard form:

• 4.67 x 103 =__________________• 3.112 x 105 = _________________• 3.112 x 10-4 = ________________• 4 x 10-6 = ___________________• 1 x 1011 = __________________

4670

311200

0.0003112

0.000004

100,000,000,000

STANDARDS OF MEASUREMENT

WHY SI UNITS?

metric• standard of measurement (for most

nations)• each type of SI measurement has a base

unitbase unit• fundamental unit of measurement which

are used to form other, compound units for other quantities. (SI base unit)

What does SI stand for?

international system of units

SI PREFIXES

Easy to use because it is based on multiples of ten.

Prefix Symbol Multiplying factor

giga G 1000000000 or 109

mega M 1000000 or 106

kilo k 1000 or 103

hecto h 100 or 102

deka da (dk) 10 or 101

Base unit 0

deci dc .1 or 10-1

centi c .01 or 10-2

milli m .001 or 10-3

micro µ .000001 or 10-6

nano n .000000001 or 10-9

K H D O D C M

• Changing from one metric unit to another is called metric conversion

• “M” is the space where meter, liter, or gram belongs or base unit (0)

• Let’s practice!• To change from one metric unit to another, we simply

move the decimal point.• For example:

25.4 km = ? cm• K-H-D-O-D-C is 5 places to the right• 25.4 km = 2,540,000 cm

K H D O D C M

• 30 cm = ? hm• C – D- O –D- H is 4 places to the left• 30 cm = 0.0030 hm

(this is the same as 0.003 hm)• 14 dal = _____dl • D- O –D is 2 places to the right• 14 dal = 1400 dl• Find the difference between the exponents of the two

prefixes.• Move the decimal that many places.

SI Prefix Conversions

20 cm = _______m

0.032 A = _______ mA

45 m = _______ nm

805 dm = _________ km

0.2

0.0805

45,000

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