Chapter 2

Measurements and Calculations

2.1 Scientific Method

◦ Observe/Collect Data

◦ Hypothesis

◦ Test/Experiment

◦ Theorize

System

◦ Specific matter in a given space that is selected to be studied.

2.2 Units of Measurement

Qualitative

◦ Given results in a descriptive non-numerical form.

◦ General observations describing the object.

Quantitative

◦ Given results in a definite form, usually numerical.

◦ Precise observation using number values.

SI measurement

International System of Units (S.I.)

◦ Le Systeme International d`Unites.

◦ Table 1 lists all base units page 34

Mass vs. Weight

◦ Mass – kilogram (kg), measures the amount of

matter.

◦ Weight – is the force of gravity on a sample of

matter.

Derived Units

Combination of two or more SI base units.

◦ Volume = amount of space occupied by an object.

length x width x height = (m3)

Liquid Volume – (mL)

◦ Density = ratio of mass to volume.

V

mD

Conversion Factors

Ratio derived from the equality between two

different units, that can be used to convert from

one to the other.

◦ 1 dollar = 4 quarters

dollar 1

quarters 4or

quarters 4

1dollar

Dimensional Analysis

Mathematical technique to help solve

problems using conversion factors.

dollars 11.25

quarters 4

1dollar

1

quarters 45x

Metric System

The International System of Units

Standard

Based upon tens or decimal places.

Used throughout the world.

Table of Prefixes Prefix Abbrev. Meaning

Tera- T 1012

Giga- G 109

Mega- M 106

kilo- k 103

hecto- h 102

deca- da 101

Base Units - meter, liter, gram, or second

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- µ 10-6

nano- n 10-9

pico- p 10-12

Metric Conversions

Convert 50 kg to g.

Convert 30 cm to m.

Metric Conversions

Identify the conversion factors needed to

convert cm to mm.

Identify the conversion factors needed to

convert cm3 to mm3.

Conversion of Cubic Units of

Volume Practice

◦ 1) 1.2 x 10-3 nm3 = ? mL

◦ 2) 1.4 x 10-2 m3 = ? mm3

2.3 Using Scientific Measurements

Accuracy

◦ How close a single measurement comes to the

actual dimension or true value.

Precision

◦ How close several measurements are to the

same value.

Page 44 – Dart board illustration

Percentage Error

accepted

acceptedexperiment

Value

Value Value error %

Error in Measurement

Measurements always contain some

degree of error.

+/- .5 error

Significant Figures

In a measurement include all the digits that

are known precisely plus one last digit that

is estimated.

Page 47 - Rules for Significant Figures

Significant Figures

Rules for significant digits: ◦ All non-zero digits are significant.

1234 5663 121112

◦ Zeroes in between two non-zero digits are always significant. 103 1004 102003

◦ Zeroes after a non-zero digits are only significant if the number has a decimal. 200. 3450. 10.

◦ Zeroes after non-zero digits are not significant if the number has no decimal. 200 40020 4230

◦ Zeroes in front of non-zero digits are never significant. .00004 0.0343 .00430

Sig Figs in Calculations

An answer can’t be more precise than the

least precise measurement from which it

was calculated.

Multiplication & Division

◦ Round all answers to the fewest sig fig.

Addition & Subtraction

◦ Round to the same number of decimal places as

the measurement with the least precision.

Sample Problems

1) (5.232x106 mm )(4.33x102mm)=

2)

3) 4.33x102cm + 1.2x102cm=

4) 7.90 kg – 4.2 kg=

L 8.2x10

g5.44x104

7

Scientific Notation

Scientific Notation or Exponential

Notation

◦ Written as the product of two numbers.

Coefficient and a power of 10.

◦ n. x 10e

◦ Where n is a digit 1-9. e is the exponent.

Proportions

Directly Proportional

◦ Dividing one quantity by the other gives a

constant value.

Inversely Proportional

◦ Product of two quantities are constant values.

Density

Density is the mass per unit of volume.

D = m/v

Density Lab

Line of best fit.

Excel graph for each metal.

Excel Graph example