Scientific Measurement and Conversions /

Dimensional Analysis

Using and Expressing Measurements

Measurement A quantity that has both a NUMBER and a UNIT

From now on: units are metric*

Scientific Notation Product of a coefficient and 10 raised to a power

Coefficient must be 1 ≤ # ≥ 9 100 = 1 101 = 10 Use “EE” or “EXP” or “E” button

means “times 10 to the”

Accuracy, Precision, and …

Accuracy How close a measurement comes to the actual or true

value of whatever is measured How close to the bulls-eye did your dart(s) land?

Precision How close a series of measurements are to one

another How close together are all your darts? (regardless of

proximity to bulls-eye)

What darts?

And …. Error

Error = experimental value – accepted value Exp value = measured in lab Accepted value = correct value based on references or

math (formulas)% error = l error l x 100 %

accepted % error = (the absolute value of experimental error –

accepted value) divided by the accepted value, times 100 to make it a %

Significant Figures

ALL “known” digits + 1 “estimated” digit Known are digits clearly marked by instrument

increments Estimated is the smallest increment divided by 10

So if ruler marks off millimeters (0.001 m) then the unknown digit will be the ten-thousandths’ place (0.0001 m)… or 0.1 mm

Sig figs can be annoying, but it is important to only record measurements to the most or least precise it can be…

Visual example…

Rules … you’re given a measurement, are the digits sig?

NONZERO digits are significant – always! 1998 m = 4 sig figs

EMBEDDED zeros are significant – always! 2002 L = 4 sig figs

LEADING zeros are NEVER significant 0.08 g = 1 sig fig

(because could be written as 8 X 10-2 g…clearly 1 sig fig)

Trailing zeros are NOT sig, UNLESS a decimal point is involved 2010 mg = 3 sig figs, BUT 201.0 cg = 4 sig figs; 2010. mg = 4 sig figs

although that format is frowned upon because it could and should be written as 2.010 x 103 mg (obviously 4 sig figs still)

Unlimited number of sig figs? Woohoo!

Counted numbers 24 students in the classroom 5 “digits” on my hand

Defined quantities 60 minutes = 1 hour 100 pennies = 1 dollar 100 cm = 1 m

Rounding- you’re not in math class anymore…

If digit ≤4, truncate (drop) 2.22 cm 2.2 cm

If digit > 5, round up 1.68 cm 1.7 cm

If digit = 5, look at numbers after OR before If there is a NONZERO digit AFTER a 5, round the 5 up (ex: 1.251 cm 1.3 cm) If there is a ZERO or NO DIGIT after a 5, look at the digit BEFORE

If digit is EVEN, truncate 5 (ex: 1.250 cm 1.2 cm) If digit is ODD, round up (ex: 1.15 cm 1.2 cm)

Mo Rounding!

Sig Figs in calculations = more rules

A calculated answer can NEVER be more precise than the least precise measurement from which it is calculated Think “a chain is only as strong as its weakest link”

Addition & Subtraction Keep the LEAST number of DECIMAL PLACES

1.8 mL + 2 mL = 3.8 mL 4 mL (must round to “ones”)

Multiplication & Division Keep the LEAST number of SIGNIFICANT FIGURES

1.8 m X 2.71 m = 4.878 m2 4.9 m2 (must round to 2 figures) Yes, PEMDAS is still in effect

Addition & Subtraction practice

Mult & Div practice

QUESTIONS??

Dimensional Analysis

Dimensional Analysis uses MULTIPLICATION and SIMPLE CONVERSION FACTORS to move from one unit to another.

Convert 2 feet to inchesWe need a conversion factor, a relationship

between the units

Dimensional Analysis

These both give us a relationship between in. and ft.

We use D.A. to cancel units

Dimensional Analysis

The units cancel out leaving only

Giving us an answer of 24 in.

Dimensional Analysis

Convert 48 inches to feet.

Dimensional Analysis

Convert 5 days to hours.

Dimensional Analysis

How many seconds are there in 4 minutes?

Dimensional Analysis

Sometimes our conversion requires more than 1 step.

Convert 1 Ms to hr.

Dimensional Analysis

Convert 60 miles/hour to feet/second

Other Common Chemistry Conversions…Temperature

K = C + 273

K Kelvin – SI Base unit of temp.

0 Kelvin = Absolute Zero – point at which all motion ceases!!

Questions??

What is Density?

Density = Mass / Volume

Table 3.6 (3.7 DNE) page 90

Solids & Liquids Gases

Material Density @ 20°C

Material Density @ 20°C

Gold 19.3 g/cm3 Chlorine 2.95 g/cm3

Mercury 13.6 g/cm3 Carbon dioxide 1.83 g/cm3

Lead 11.4 g/cm3 Argon 1.66 g/cm3

Aluminum 2.70 g/cm3 Oxygen 1.33 g/cm3

Table Sugar 1.59 g/cm3 Air 1.20 g/cm3

Corn syrup 1.35-1.38 g/cm3 Nitrogen 1.17 g/cm3

Water (4°C) 1.000 g/cm3 Neon 0.84 g/cm3

Corn oil 0.922 g/cm3 Ammonia 0.718 g/cm3

Ice (0°C) 0.917 g/cm3 Methane 0.665 g/cm3

Ethanol 0.789 g/cm3 Helium 0.166 g/cm3

Gasoline 0.66-0.69 g/cm3 Hydrogen 0.084 g/cm3

Metric (goes hand-in-hand with SI: The International System of Units)

Based on powers of 10Common units [with prefixes if needed]

Meter (length) Gram (mass) Second (time) Liter (volume)

If measuring a large item, use a larger unit If measuring tiny item, use a smaller unit

“Ken Hates Dates because Dates Cost MONEY!”Strategy 1: Stair-Step Method

kilo-

k hecto-

1000103

h deka-

100102

da m, L, g

10101

BasicUnit

deci-

100 d centi-

0.110-1

c milli-

0.0110-2

m

0.00110-3

How Do I Use This?

The first letter tells you which step to start on.

The first letter tells you which step to stop on.

Count the number of steps to get to where you need to stop.

If you went downstairs the decimal moves that many places to the right

How Do I Use This (cont.)?

If you went upstairs the decimal moves to the left. Fill any empty places with zeros.

If there is only one letter in the unit of measurement, then you start or stop on the base unit step. Now let’s look at our examples…..

525568 mm = ? m

.00654 km = ? m

Strategy 2: Conversion Factors (YOU MUST KNOW HOW TO DO IT THIS WAY!)

•Used to convert the same quantity of something to a new unit•Ex: 1 mL = 1 cm3 (or 1 cc)

Practice Writing Conversion Factors:

Mo metric conversion

Again, again!

Questions??