Ch. 3, Scientific Measurement
Measurement
•
: A quantity that has a
and a
. Like 52 meters.
Scientific Notation
• Writing long numbers as smaller ones to a
power of ten.
•
=
1.4 x 106 = 1.4E6
• .00056 =
= 5.6E-4
• 15,093,000 = 1.5093 x 107 =
Accuracy vs. Precision
• *
: How
close a measurement
comes to the
value.
• *
: How
close a series of
measurements are to
.
Determining Error of a measurement
•
= Experimental Value - Accepted Value
– Can be positive or
• Percent Error = error / accepted value * 100%
– or
– Always
• Example, you measured 99 cm, but it is 100 cm.
•
: The digits in a
measurement that are known plus one
that is not known.
– Filled 43.1 mL
Rules for Sig Figs
• Non-Zero Numbers are always significant
– Ex) .236 m has
sig figs.
• Zeros between non-zero numbers are significant.
– Ex) 7003 m and 40.79 m each have
sig figs.
• Leftmost zeros are not significant
– Ex) .000099 m, 0.42 m, and .073 m each have
sig figs.
• Rightmost zeros are significant if they come before or after
a period.
– Ex) 9000. m, 90.00 m, and 9.090 m each have
sig figs.
Rules for Sig Figs
• Rightmost zeros with no decimal points are no
significant.
• Ex) 300 m has
sig fig.
• Exactly defined quantities have an
number of sig figs.
• Seen most when converting between
measurements.
• 60 min = 1 hour, 100 cm = 1 m each have an
unlimited number of sig figs.
Is a Zero a Significant Number or Not?
•
•
•
•
504 L
.06 mL
50.0 m
7,000 km
Sig Figs in Calculations:
• Calculations
be more precise than the
precise measurement.
• Addition or subtraction - Round the final answer to the
same number of decimal places as the measurement with
the
number of decimal places.
– the last “shared column”.
• 13.4 m + 5.254 m = 18.7 m
Sig Figs in Calculations:
• Multiplication or Division - The final answer
should have the
number of sig figs
as the measurement that has the
number of sig figs.
• 2.4526 m x 8.4 m = 21 m
• In this class, delay rounding until the very end.
• (3.449L + 6.57L) * 8.779L / 5.2L = 17L
International System of Units
• How much of
something you have is
given by Units. Like
centimeters, kilometers,
etc.
•
is the standard
measurement system
for science.
•
•
•
•
•
•
•
* The five SI units used most by chemists are:
Distance =
(m)
Mass = kilogram (kg)
Temperature =
(K)
Time = second (s)
Volume = liter (L)
Amount =
(mol).
• Prefixes can be used in front of units for
powers of 10.
•
= how much “stuff”
is in something. How much
matter is in something.
•
= the pull on
something by gravity.
• If I go to the moon, which
changes and which stays
constant?
changes,
stays the same.
Temperature:
• Celsius and Kelvin are units of temperature
that are the
, just shifted.
• K = C + 273
• Water freezes at 0 C and at
K.
• Absolute Zero = 0 K;
a K value will never be
negative.
*Energy
• *
- The ability to do work or
produce heat.
•
(J) is the SI unit of energy.
•
• 1 J = .239 cal
(cal) is another unit of energy.
Conversions
Convert 7 mm to m.
Convert 12.4 Mm to cm.
• Convert 7 km/ms to m/s
• An experiment asks students to measure 1.50 g
of Cu wire. All we have is a 40.0 g spool of Cu.
How many students can do the experiment?
*Density
• *
= mass / volume
• What is the density of 2 g of salt in a volume
of 4 L?
• What is the density in g/L of 5 kg of salt in a
volume of 6 mL?
If silver has a density of 10.5 g/L, what is
the volume of a silver coin that has a
mass of 14 g?
• Density
as temperature increases.
• D=m/v
• As T increases, V
• Therefore, density decreases.
.
Example Problems!!!
• 1. How many sig figs in: 1.480*105
.00070
1.000080
3.00E3
• 2. Perform these calculations and come up with answers
that have the correct number of sig figs:
5.667 + .34
5.007E3 / 1.20
4.3 - 1.3590
5.309E3 * 3
• 3. Convert 3.4 ng into kg.
• 4. Convert 7E3 cm into Mm.
• 5. What is the mass if a substance with a density of
4.5 g/L has a volume of 3 L?
6. How many sig figs in:
1010
3000
3000.
3000.0
7. Convert 3 kg into g.
Convert 34 cm into m.
Convert 4 m into cm.
8. You have a 4 kg box. You measure it to be 5.8 kg. What
is the error? The % error?
9. What is the difference between mass and weight?
Accuracy and precision?
• 11. Put 5,009,000,000 into Scientific Notation
• 12. Put 0.00007890 into Scientific Notation.
• 13. Put 8.7 * 10-4 into a regular number.
• 14. Which is the largest amount?
• A. 2*102 g
B. 30 kg
C. 45 mg D. 190 g
• 15. Convert 40 Kelvin into Celsius
• 16. Convert 99 Celsius into Kelvin.
More from Chp 3
• I. Using Measurements
A. Accuracy vs. Precision
•
- how close a
measurement is to the accepted value
•
- how close a
series of measurements are to each
other
ACCURATE = CORRECT
PRECISE = CONSISTENT
C. Significant Figures
• Indicate precision of a measurement.
• Recording Sig Figs
– Sig figs in a measurement include the
digits plus a final
– (See page 24)
2.32 cm
_
digit
• 1) How many sig figs
after we estimate?
• 2) Now how many?
C. Significant Figures
• Counting Sig Figs
– Count all numbers EXCEPT:
• _______________zeros -- 0.0025
• Trailing zeros _________________
a decimal point -- 2,500
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
sig figs
2. 402
sig figs
3. 5,280
sig figs
4. 0.080
sig figs
C. Significant Figures
• Calculating with Sig Figs
– Multiply/Divide - The # with the
sig figs determines the # of sig figs in the
answer.
(13.91g/cm3)(23.3cm3) = 324.103g
C. Significant Figures
• Calculating with Sig Figs (con’t)
– Add/Subtract - The # with the
decimal value determines the place of the last sig
fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL 
C. Significant Figures
• Calculating with Sig Figs (con’t)
– Exact Numbers do not limit the # of sig figs in
the answer.
• Counting numbers: 12 students
• Exact conversions: 1 m = 100 cm
• “1” in any conversion: 1 in = 2.54 cm
C. Significant Figures
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
= 2.390625 g/mL 
6. 18.9 g
- 0.84 g
18.06 g
D. Scientific Notation
65,000 kg  6.5 × 104 kg
• Converting into Sci. Notation:
– Move decimal until there’s
Places moved =
– Large # (>1) 
Small # (<1) 
– Only include sig figs.
digit to its left.
.
exponent
exponent
D. Scientific Notation
Practice Problems
7. 2,400,000 g
8. 0.00256 kg
9.
7  10-5 km
10. 6.2  104 mm
D. Scientific Notation
• Calculating with Sci. Notation
(5.44 x 107 g) / (8.1 x 104 mol) =
Type of your calculator:
5.44 EE 7 / 8.1 EE 4 =
671.6049383
E. SI Units
Quantity
Symbol
Base Unit
Length
l
meter
Mass
m
kilogram
Time
t
second
s
kelvin
K
Temp
Amount
n
mole
Abbrev.
E. SI Units
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
F. Derived Units
• Combination of base units.
•

(m3 or cm3) 1 cm3 = 1 mL
– length  length  length
(kg/m3 or g/cm3)
mass per volume
1 dm3 = 1 L
M
D=
V
Problem-Solving Steps
1.
_
2. Plan
3. Compute
4.
_
Density
• An object has a volume of 825 cm3 and a
density of 13.6 g/cm3. Find its mass.
GIVEN:
WORK:
V=
D=
M=?
M=
M=
M
D
V
M=
Density
• A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
WORK:
D=
V=?
M=
V=
M
D
V
V=
V=
SI Prefix Conversions
move right
move left
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
SI Unit Conversions
• King __doofus can milk many newts.
• k__ d c m m n
• kilo, deci,
• What’s yours?
, milli,
,
SI Prefix Conversions
532 m
NUMBER
UNIT
= _______ km
NUMBER
UNIT
=
SI Prefix Conversions
1) 20 cm =
______________ m
2) 0.032 L = ______________ mL
3) 45 m =
____
mm
4) 805 dm = ______________ km
Dimensional Analysis
• Steps:
1. Identify starting &
units.
2. Line up conversion factors so units
3. Multiply all
numbers & divide by each
bottom number.
4. Check units & answer.
.
Dimensional Analysis
• Lining up conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
Dimensional Analysis
• How many milliliters are in 1.00 quart of
milk? (1L = 1.057 qt)
qt
mL
1.00 qt

Dimensional Analysis
• You have 1.5 pounds of gold. Find its
volume in cm3 if the density of gold is 19.3
g/cm3. (1 kg = 2.2 lbs)
lb
1.5 lb
cm3
Dimensional Analysis
5) Your European hairdresser wants to cut
your hair 8.0 cm shorter. How many
inches will he be cutting off? (1 in=2.54cm)
cm
in
8.0 cm