MEASUREMENT

Accuracy and Precision

• All measurements are affected by errors.

• Measurements are always subjected to some uncertainty.

• This uncertainty can be expressed as accuracy or precision.

Reasons for Uncertainty

• The limitations inherent in the construction of the measuring instrument.

• The conditions under which the measurement was made.

• The different ways in which the person uses or reads the measuring instrument.

ACCURACY

• It is the closeness of a measurement to the accepted value for a specific physical quantity.

• It can be expressed as Absolute error or Relative error.

ACCURACY: Absolute Error• it is the actual difference

between the measured value and the accepted value.

• EA = /O-A/

EA = Absolute error

O = Measured/Observed valueA = Accepted value

ACCURACY: Relative Error• it is the percentage error• ER = (EA / A) * 100

ER = Relative error

EA = Absolute error

A = Accepted value

PRECISION

• It is the agreement among several measurements that have been made in the same way.

• It tells how reproducible the measurements are and expressed in terms of Deviation.

PRECISION: Absolute Deviation• it is the difference between a

single measured value and the average of several measurements made in the same way.

• DA = /O-M/

DA = Absolute deviationO = Measured/Observed valueM = Mean of several readings

PRECISION: Relative Deviation• it is the percentage average

deviation of a set of measurements

• DR = (DA average / M) * 100

– DR = Relative deviation

– DA average = average DA of a set of

measurement

Let’s have a quiz

Trial Mass Absolute Error (Ea)

Relative Error (Er)

Absolute Deviation (Da)

Relative Deviation

1 13.26

2 13.18

3 12.95

Accepted Value is 13.20 grams

MEASUREMENT

• not only common in science-related fields but also in everyday lives

• It means comparing anything with a standard to find out the number of times that that standard is contained in the object.

• Ex.: the table is three meters long

Fundamental Quantities/Units• simplest quantities and units

that are convenient to use as basis for explaining or defining

• There are seven fundamental quantities and units.

Fundamental Quantities/Units

• Length meter m• Mass kilogram kg• Time second s• Temperature Kelvin K• Electric current Ampere A• Amount of substance mole

mol• Luminous intensity Candela cd

Derived Quantities/Units• quantities and units defined in

terms of the fundamental quantities and units

Derived Quantities/Units

• Volume cubic meter or liter m3, L

• Density kilogram per cubic meterkg/m3

meter per liter m/L• Speed/velocity meter per second

m/s• Concentration moles per cubic meter

mol/m3

• Force Newton N• Energy Joule J• Power Watt W

System of Units

• As a result of scientific progress and different choices of base units, attempts have been made to create a metric system.

• The modern metric system (1960) is now widely used throughout the world.

System of Units

• Traditionally, the English system was used (foot, gallon, and pound).

• In the modern days, System Internationale d’ Unites (Sevres, France)

• International System of Units (Metric System)

Metric System

• system of measurement that uses the unit meter as standard for length, kilogram for mass and second for time.

• Advantage is it uses decimal system.

• Some units are just multiples or submultiples of ten.

Metric System

• It has branched out to two systems:– MKS (meter-kilogram-second)– CGS (centimeter-gram-second)

• The metric system is easier to learn, remember and apply.

SystemQuantity

Length Mass Time

Englishfps

Foot(ft)

Pound(lb)

Second(sec)

cgsCentimet

er(cm)

Gram(g)

Second(sec)

Metricmks

Meter(m)

Kilogram(kg)

Second(sec)

Common Prefixes used in Metric System

• Nano n 10-9 (billionth)• Micro μ 10-6 (millionth)• Milli m 10-3 (thousandth)• Centi c 10-2 (hundredth)• Deci d 10-1 (tenth)• Deka dk 101 (ten)• Hector h 102 (hundred)• Kilo k 103 (thousand)• Mega M 102 (million)• Giga G 103 (billion)

Common Prefixes used in Metric System• These prefixes can be use with

any of the units to expressions like:

1 nm = 10-9 m1 Ms = 109 s

Conversion of Units

• It will be helpful to know how the magnitude of the SI units compare with each other or the English system with the Metric system and vice versa.

• To find such, we use conversion of units.

Dimensional Analysis

• Also called the factor-label method or unit-factor method

• It is a sequential application of conversion factors expressed as fractions

Dimensional Analysis

Given x conversion = desiredquantity factor

quantity

CONVERSION FACTORS

Mass1 kg = 1000 g = 2.2 lbs1 ounce = 28.35 g

Length1 m = 100 cm = 39.4 in =

3.28 ft1 mi = 1.61 km = 5280 ft1 in = 2.54 cm1 yard = 3 ft

CONVERSION FACTORS

Volume1 L = 1000 cm3 = 1000 ml = 1.06 qrt

1 gal = 3.79 L

For Temperature

• Since the standard measuring device for temperature is thermometer, and it is never marked a Kelvin, conversion of units is applied.

For Temperature

•TF = 1.8Tc + 32

•TC = (TF – 32)/1.8

•TK = Tc + 273.15 K