Units Of Measurement

Mrs. Mawhiney

Measurement of mass, length and volume

• In the United States, we use a fairly awkward system of measurement for most things - the English system Scientists use the metric and SI systems of units for the measurement of physical quantities

• This system using standard units based on very precisely known properties of matter and light

• Prefixes are used in from of the units to indicate powers of ten

SI Units

Measurement Unit Symbol

Mass Kilogram kg

Length Meter M

Time Second s

Temperature Kelvin K

Quantity Mole mol

Energy Joule J

Pressure Pascal Pa

. Base Units

Mass - the quantity of matter that a sample contains

• Note that weight is a measure of the attraction of gravity for a sample and it varies depending on the distance of the mass to a planet or moon

• Scientists often speak imprecisely of the “weight” of an amount of substance. They really mean mass.

Basic SI units/Derived units

Used to generate new Units• Volume - space a given quantity of matter

occupies• Volume - expressed in terms of length - m3

• m3 - an inconveniently large volume, so we use liter (L; one cubic decimeter)

• We often use a mL (1 cubic centimeter) for more manageable amounts of matter

Converting between units

• The standard method to convert between two different units is the factor-label or dimensional analysis method

• Dimensional analysis converts a measurement in one unit to another by the use of a conversion factor

• Conversion factors are developed from relationships between units

Measurements and Units

Measurement - determines the quantity, dimensions or extent of something1.Consist of two parts

a. a numerical quantity (1.23)b. a specific unit (meters)

Unit - a definite quantity adapted to as a standard of measurement

Features of Measured Quantities

When we measure a number, there are physical constraints to the measurement

Instruments and scientists are not perfect, so the measurement is not perfect (i. e., it has error)

The error in the measurement is related to the accuracy and the precision of the measurement

Accuracy and Precision

Accuracy – how close the measurement is to the “true” value (of course we have to know what the “true” value is)

Precision – is a measure of how closely individual measurements agree with one another.

Example: Accuracy and Precision

Equations for Precision and Accuracy

1. Precision

2. Accuracy

Absolute Error

% AE = (True value-Avg Value) X 100

True Value

Significant Figures•Any digit that is not zero is significant

1.234 kg 4 significant figures

•Zeros between nonzero digits are significant

6006 m 4 significant figures

•Zeros to the left of the first nonzero digit are not significant

0.08 L 1 significant figure

•One or more final zeros to the right of the decimal point are significant

2.00 mg 3 significant figures

0.00420 g 3 significant figures

10.006000 8 sig figs

Counting Significant FiguresAtlantic / Pacific Method

a. Absent Decimal- Start on “atlantic” side of number & cross out all zeroes until 1st nonzero digit is reached, remaining digits are significant

b. Present decimal- start on the “pacific” side of the number & cross out all zeros until the 1st nonzero digit Is reached, remaining digits are significant

How many significant figures are in each of the following measurements?

24 mL 2 significant figures

3001 g 4 significant figures

0.0320 m3 3 significant figures

6.400 x 104 molecules 4 significant figures

560 kg 2 significant figures

Significant Figures

Addition or Subtraction

The answer cannot be more accurate than any of the original numbers.

89.3321.1+

90.432 round off to 90.4

one significant figure after decimal point

3.70-2.91330.7867

two significant figures after decimal point

round off to 0.79

370-291.33 78.67

Number is rounded to “tens” place

round off to 80

Significant Figures

Multiplication or Division

The number of significant figures in the result is set by the original number that has the smallest number of significant figures

4.51 x 3.6666 = 16.536366 = 16.5

3 sig figs round to3 sig figs

6.8 ÷ 112.04 = 0.0606926

2 sig figs round to2 sig figs

= 0.061

Significant Figures

Exact Numbers

Numbers from definitions or numbers of objects are consideredto have an infinite number of significant figures

The average of three measured lengths; 6.64, 6.68 and 6.70?

6.64 + 6.68 + 6.703

= 6.67333 = 6.67

Because 3 is an exact number

= 7

Scientific notation and significant figures

1. When using scientific notation the base must be written with the correct number of significant digits

2. All zeroes are significant when using scientific notation