MeasurementsScientific NotationSignificant Figures

1795 French scientists adopt system of standard units called the metric system.

In 1960 the metric system was revised to the SI system.◦ Systeme Internationale d’Unites

Base Units◦ Time – second◦ Length – meter◦ Mass - kilogram

SI System

Defined unit in a system of measurement that is based on an object or event in the physical world.

Independent of other units.

Base Units

Quantity Base UnitTime Second (s)Length Meter (m)Mass Kilogram (kg)Temperature Kelvin (K)Amount of a Substance Mole (mol)Electric Current Ampere (A)Luminous Intensity Candela (cd)

Base Units

Unit that is defined by a combination of base units.◦ Volume – the space occupied by an object.

derived unit – m3

cm3 = mL◦ Density – ratio that compares mass of an object to

its volume.

Derived Units

3cmg or mL

g

How can we rearrange this equation if we have the density and volume.

Density

volumemassdensity

massvolumedensity

Kelvin scale, founded by William Thompson who was known as Lord Kelvin.◦ Water freezes at 273 K◦ It boils at 373K◦ The scale is the same as Celsius, just different

temperature points Celsius + 273 = Kelvin

Kelvin – 273 = Celsius

Temperature

If the density of an object is 2.70 g/cm3 and the mass of the object is 1.65g, what is the volume of the sample?

Problems

vmD

Dmv

370.2

65.1

cmggv

3611.0 cmv

Convert the following:◦ 357oC to Kelvin

357oC + 273 = 630K

◦ -39oC to Kelvin -39oC + 273 = 234K

◦ 266K to Celsius 266K – 273 = -7oC

◦ 332K to Celsius 332K – 273 = 59oC

Problem

A visual display of data.

Circle Graphs or Pie Charts◦ Show parts of a fixed whole◦ Usually broken into %

Bar Graphs◦ Show how quantities vary◦ Measured quantity on y-axis◦ Independent variable on x-axis

Graphs

Line Graphs◦ Most common in chemistry◦ Independent variable on x-axis◦ Dependent variable on y-axis◦ Can determine slope of line

Graphs

xy

xxyyslope

12

12

PrefixesSI Prefixes

mega (M) 106

kilo (k) 103

basic unitdeci (d) 10-1

centi (c) 10-2

milli (m) 10-3

micro (µ) 10-6

nano (n) 10-9

pico (p) 10-12

Expresses numbers as a multiple of two factors:◦ A number between 1 and 10.◦ Ten raised to a power or exponent.

Exponent tells you how many times the first factor must be multiplied by 10.

A number larger than 1 expressed in scientific notation, the power of 10 is positive.

A number smaller than 1 has a negative power of 10.

Scientific Notation

Express the following in scientific notation

Put the following scientific notation numbers in standard notation.

Problems

m4108.3

kg51087.6

g81028.1

m000,38

kg0000687.0

g000,000,128m31094.8 m00894.0

When multiplying terms in scientific notation, you multiply the coefficients, keep your base of 10 and add the exponents.

When dividing terms in scientific notation, you divide the coefficients, keep your base of 10 and subtract the exponents.

Multiplying and Dividing with Scientific Notation

Multiplying and Dividing

25 100.5100.3 25100.50.34105.1

2

5

100.1105.3

25100.15.3 3105.3

When adding or subtracting in scientific notation:◦ Get terms to have the same exponent.◦ Add or subtract the coefficients.◦ Keep your base of ten.◦ Keep the exponent that both terms contained.

Addition and Subtraction with Scientific Notation

Adding and Subtracting

32 107.5103.8

33 107.51083.0

3107.583.031053.6

Indicate the uncertainty of a measurement.

Include all known digits plus one estimated digit.

Significant Figures

All non-zero digits are significant.◦ 127.34 ◦ Contains 5 significant digits.

All zeros between two non-zero digits are significant.◦ 120.007◦ Contains 6 significant digits.

Unless specifically indicated by the context to be significant, ALL zeros to the left of an understood decimal point, but to the left of a non-zero digit are NOT significant.◦ 109,000◦ Contains 3 significant digits

Rules for Significant Figures (Digits)

All zeros to the left of an expressed decimal point and to the right of a non-zero digit ARE significant.◦ 109,000.◦ Contains 6 significant figures.

All zeros to the right of a decimal point, but to the left of a non-zero digit are NOT significant.◦ 0.00476◦ Contains 3 significant figures.

The single zero conventionally placed to the left of the decimal point is NEVER significant

Rules continued…

ALL zeros to the right of the decimal point and to the right of a nonzero digit ARE significant.◦ 0.04060◦ 30.00◦ Both contain 4 significant digits.

Counting numbers and defined constants have an infinite number of significant digits.◦ 60 s = 1 min◦ 11 soccer players

Rules continued…

Multiplication and Division◦ The answer contains the same number of

significant figures as the measurement with the least amount of significant figures.

Addition and Subtraction◦ The answer has the same number of decimal

places as the measurement with the least amount of decimal places.

Operations with Significant Figures

Precision◦ The agreement between measurements.◦ How close a set of measurements are to each

other.

Accuracy◦ The nearness of a measurement to its actual

value.◦ How close you are to the true value.

Precision vs. Accuracy

Precision vs. Accuracy

These thermometers have different levels of precision. The increments on the left are 0.2, but the ones on the right are 1.0. How should their temperatures be recorded?

37.53 5.8

The ratio of an error to an accepted value.

Percent Error

100exp

%

ltheoreticaerimentalltheoretica

error

You analyze a sample of copper sulfate and find that it is 68% copper. The theoretical value of copper is 80%. What is the percent error?

Example

100806880 %15