Transcript Chapter 2 ppt.

Measurements &
Calculations
Chapter 2
Section 2.1
SCIENTIFIC NOTATION
Objective: show how very large or very small numbers can be
expressed as the product of a number between 1 and 10 AND a power
of 10
In science, we often encounter very large and very
small numbers. Using scientific numbers makes
working with these numbers easier
RULE 1
As the decimal is moved to the left
The power of 10 increases one
value for each decimal place moved
Any number to the
Zero power = 1
RULE 2
As the decimal is moved to the right
The power of 10 decreases one
value for each decimal place moved
Any number to the
Zero power = 1
Section 2.2 and 2.3
UNITS and MEASUREMENTS
OF LENGTH, VOLUME & MASS
Objective: to learn english, metric and SI systems of measurement
Section 2.3
MEASUREMENTS OF LENGTH,
VOLUME & MASS
Objective: understand metric system for measuring length, volume
and mass
Section 2.5
SIGNIFICANT FIGURES
Objective: to learn how to determine the number of sig figs
Significant Figures




All number other then zero are significant
 Ex. 23 = 2 sig figs
Leading zeros- zeros that are at the beginning of a number
are NEVER significant
 Ex 034 = 2 sig figs
and .0578 = 3 sig figs
Trapped zeros – zeros that are trapped between two other
significant figures are ALWAYS significant
 Ex 304 = 3 sig figs and 8.0091 = 5 sig figs
Trailing zeros – zeros that are at the end of a number –
depends on if there is a decimal point expressed in that
number
 If there is a decimal point showing in the number then the
zeros are significant
 Ex 60 = 1 si fig but 60. = 2 sig figs and 60.0 = 3 sig figs
 Ex .05 = 1 sig figs
 If there is NOT a decimal point showing in the number
then the zeros are NOT sinificant
Example:
120000
120000
.
No decimal
point
2 sig figs
Zeros are not
significant!
Decimal
Point
All digits including
zeros to the left of
The decimal are
significant.
6 sig figs
All figures are
Significant
4 sig figs
All figures are
Significant
5 sig figs
Zeros between
Non zeros are
significant
Zero to the
Right of the
Decimal are
significant
3 sig figs
Zeros to the right of
The decimal with no
Non zero values
Before the decimal
Are not significant
5 sig figs
Zeros to the right of the decimal
And to the right of non zero values
Are significant
Exact equivalences have an unlimited number of
significant figures
Therefore in the statement 1 in = 2.54 cm,
Neither the 1 nor the 2.54 limits the number of
Sig figs when used in a calculation
The same is true for:
Exact numbers
(numbers that were not obtained using measuring
devices, but determined by counting)
also have an unlimited number of sig figs
Examples:
3 apples
8 molecules
32 students
Section 2.4
UNCERTAINTY IN MEASUREMENT
Objective: to understand how uncertainty in measurement arises
Difference between accuracy and precision
Significant Figures



Significant figures are used to distinguish truly measured values from those
simply resulting from calculation. Significant figures determine the
precision of a measurement. Precision refers to the degree of subdivision of
a measurement.
As an example, suppose we were to ask you to measure how tall the school
is, you replied “About one hundred meters”. This would be written as 100
with no decimal point included. This is shown with one significant figure the
“1”, the zeros don’t count and it tells us that the building is about 100 meters
but it could be 95 m or even 104 m. If we continued to inquire and ask you to
be more precise, you might re-measure and say “ OK, ninety seven meters.
This would be written as 97m. It contains two significant figures, the 9 and
the 7. Now we know that you have somewhere between 96.5m and 97.4m.
If we continue to ask you to measure even more precise with more precision,
may eventually say, “97.2 m”.
THE PRECISION OF YOUR MEASUREMENT IS DICTATED BY THE
INSTRUMENT YOU ARE USING TO MEASURE!!!!
ACCURACY MEANS HOW CLOSE A MEASUREMENT
IS TO THE TRUE VALUE
PRECISION REFERS TO THE DEGREE OF
SUBBDIVISION OF THE MEASUREMENT
FOR EXAMPLE, IF A ROOM IS 10 FEET LONG AND
YOU MEASURE IT TO BE 15.9134 FT LONG, YOUR
MEASUREMENT IS VERY PRECISE BUT INACCURATE !
MEASUREMENTS SHOULD BE ACCURATE AND AS
PRECISE AS THE MEASURING DEVICE ALLOWS
Illustration of accurate vs percise
You tell me. What is it?
Measurements are always all measured values plus one
approximated value. The pencil is 3.6 cm long.
1
3
2
3
4
4
5
7
With more calibration a more
precise measurement is possible
The pencil is 3.64 cm long!
3.6
The calibration of the instrument
determines measurement precision
6
3.7
Now 3.640 cm !
What is the precision on a ruler?
Follow directions from Mrs McGrath & try
to figure it out???
 What if your measurement was in cm?
 What if your measurement was in mm?

Scales and sig figs

In our class
 Write
down what the
scale says
 Most scales are taken
to the hundreths place
Graduated Cylinders & Thermometers
First – figure out scale
Then – take measurement
out to one guess past
certainity
Section 2.5 continued
MATH AND SIG FIGS
RULES FOR ROUNDING OFF
Round each number to one sig fig:
If the digit is to be removed:
Is less than 5, the preceding digit stays the same
EX. 1.49 rounds to ???? _____________
is equal to or greater then 5, the preceding digit is increased
EX. 1.509 rounds to ???? _____________
In calculations:
carry the extra digits through to the
final result AND THEN round off
Addition/Subtraction with Sig Figs

Adding and subtracting with significant figures.
The position, not the number, of the significant
figures is important in adding and subtracting.
For example,
12.03
(the last sig fig is in hundredth place (0.01))
+ 2.0205 (the last sig fig is in ten thousandth (0.0001))
14.0505
14.05 (the answer is rounded off to
the least significant position
hundredths place)
The numbers in
these positions are
not zeros, they are
unknown
The answer is rounded to the
position of least significance
Don’t even look at
The 6 to determine
Rounding. Only
Look at the 4
Multiplying/Dividing with Significant Figures
The result of multiplication or division can have no more sig figs
than the term with the least number.
*ex. 9 x 2 = 20 since the 9 has one sig fig and the 2 has one
sig fig, the answer 20 must have only one and is written without
a decimal to show that fact.
* By contrast, 9.0 x 2.0 = 18 each term has two sig figs and the
answer must also have two.
*4.56 x 1.4 = 6.384 How many sig figs can this answer have?
6.4 (2 sig figs)
Section 2.6
DIMENSIONAL ANALYSIS
Objective: learn how to apply dimensional analysis to solve problems
NO KING HENRY


You must use
dimensional analysis
to convert from metric
to metric
You must use your
brain and logic to do
this
K H D b d c m
From the last slide we
learned the meaning of some
of the common prefixes, BUT
we are going to learn to
dimensional analysis using the
root prefixes and deciding
bigger/smaller.
Conversions YOU Need to Memorize

Length
 1in
= 2.54 cm
 39.37 in = 1 meter
 1 mile = 5280 feet

Mass
 1kg
= 2.2 lbs
 1lb = 454 grams

Volume
1
liter = 1.06qts
 1 gallon = 3.79 liters
Dimensional Analysis Rules
1.37days = ? minutes
 Always start with the known value over the
number 1
 Always write one number over the other
 Always, Always, Always, Always, Always
write/include the unit with the number


1.37 days
1
Single step
examples
 3.6 m = ? ft
 6.07 lb = ?kg
 4.2 L = ?qt
 35.92 cm = ? in
Equivalence statements
 Length




Mass



1in = 2.54 cm
39.37 in = 1 meter
1 mile = 5280 feet
1kg = 2.2 lbs
1lb = 454 grams
Volume


1 liter = 1.06qts
1 gallon = 3.79 liters
Double step
Exampls
 56,345 s = ? yrs
 98.3 in = ?m
 3.2 mi = ?km
Equivalence Statements
 Length




Mass



1m = 1.094 yd
2.54 cm = 1 in
1mi = 1760 yd
1kg = 2.205 lb
453.6 g = 1lb
Volume

1 L = 1.06qt
Section 2.7
TEMPERATURE CONVERSIONS
Objective: to learn three temperature scales
to convert from one scale to another
Temperature – the average
kinetic energy in a substance

Boiling points
 Fahrenheit
212 F
 Celsius 100 C
 Kelvin 373 K

Freezing points
 Fahrenheit
32 F
 Celsius 0 C
 Kelvin - 273 K
*O Kelvin or Absolute zero: point at which molecular motion stops
Temperature Conversion Formulas
Celsius to Kelvin
TK = TC + 273
Kelvin to Celsius
TC = TK – 273
Celsius to
Fahrenheit
Fahrenheit to
Celsius
TF = 1.80TC + 32
TC = TF - 32
1.80
Section 2.8
DENSITY
Objective: to define density and its units
Density: the amount of matter
present in a given volume of a
substance
Units
Formula

Density = mass/volume



DENSITY of a substance never changes
Ex gold is ALWAYS 19.3g/cm3
Density = g/ml OR g/cm3
Mass = g (grams)
Volume = ml OR cm3

Liquids OR
solids
Less dense objects “FLOAT” in more dense objects
Example calculation

Mercury has a density of 13.6g/ml. What
volume of mercury must be taken to obtain
225 grams of the metal?
Example calculation: ANSWER

Mercury has a density of 13.6g/ml. What
volume of mercury must be taken to obtain
225 grams of the metal?
 16.5
mL
THE END 