Ch. 3, Scientific
Measurement
Measurement
• Measurement: A quantity that has
a number and a unit. Like 52
meters.
D. Scientific Notation
65,000 kg  6.5 × 104 kg
• Converting into Sci. Notation:
– Move decimal until there’s 1 digit to its left.
– Any number other than 0.
– Places moved = exponent.
– Large # (>1)  positive exponent
Small # (<1)  negative exponent
– Only include sig figs.
D. Scientific Notation
Practice Problems
7. 2,400,000 g
2.4 
8. 0.00256 kg
2.56 
9.
6
10
g
-3
10
kg
7  10-5 km 0.00007 km
10. 6.2  104 mm
62,000 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 = 670 g/mol = 6.7 x 102 g/mol
A. Accuracy vs. Precision
• Accuracy - how close a measurement is
to the accepted value
• Precision - how close a series of
measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
Accuracy vs. Precision
• *Accuracy: How
close a
measurement
comes to the
correct value.
• *Precision: How
close a series of
measurements
are to one
another.
– Consistency
Determining Error of a measurement
• Error = Experimental Value - Accepted Value
– Can be positive or negative
• Percent Error = error / accepted value * 100%
– or
– Always positive
• Example, you measured 99 cm, but it is 100 cm.
99 cm – 100 cm
x
100
=
1%
error
100 cm
x 100
C. Significant Figures
• Indicate precision of a measurement.
• Recording Sig Figs
– Sig figs in a measurement include the known
digits plus a final estimated digit
– (See page 24)
2.32 cm
• 1) How many sig figs
after we estimate?
– 3.2
• 2) Now how many?
– 3.13
Rules for Sig Figs
• Non-Zero Numbers are always significant
– Ex) .236 m has 3 sig figs.
• Zeros between non-zero numbers are significant.
– Ex) 7003 m and 40.79 m each have 4 sig figs.
• Leftmost zeros are not significant
– Ex) .000099 m, 0.42 m, and .073 m each have 2 sig figs.
• Rightmost zeros are significant IF they come before or after a
decimal.
– Ex) 9000. m, 90.00 m, and 9.090 m each have 4 sig figs.
• Rightmost zeros with no decimal points are not significant.
• Ex) 300 m has 1 sig fig.
**The number of left handed people in the class is
insignificant compared to the number of right handed people
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
Is a Zero a Significant Number or Not?
• 504 L
YES – 3 sig figs
• .06 mL
NO – 1 sig figs
• 50.0 m
YES – 3 sig figs
• 7,000 km
NO – 1 sig fig
C. Significant Figures
• Calculating with Sig Figs
– Multiply/Divide - The # with the fewest sig figs
determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
C. Significant Figures
• Calculating with Sig Figs (con’t)
– Add/Subtract - The # with the lowest decimal
value determines the place of the last sig fig in the
answer.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 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
• In this class, delay rounding until
the very end.
• 1.8 × 2.10 × 1.542
Rounding: 1.8 x 2.10 = 3.8 x 1.542 = 5.9
Round at end: 1.8 x 2.10 x 1.542 = 5.82876 = 5.8
C. Significant Figures
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
6. 18.9 g
- 0.84 g
18.06 g  18.1 g
E. SI Units
Quantity
Symbol
Base Unit
Abbrev.
Length
l
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temp
T
kelvin
K
Amount
Volume
n
V
mole
liter
mol
L
Temperature:
• Celsius and Kelvin are units of temperature that
are the same, just shifted.
• K = C + 273
• Water freezes at 0 C and at 273 K.
• Absolute Zero = 0 K; K will never be negative.
• Convert 15 C to K = 288 K
• Convert 321 K to C = 48 C
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
Different way of looking at it…
• 1 km = 1000 m
• 1 m = 10 dm
• 1 m = 100 cm
• 1 m = 1000 mm
• 1 mm = 1000 um
F. Derived Units
• Combination of base units.
• Volume (m3 or cm3)
– length  length  length
 Density (kg/m3 or g/cm3)
mass per volume
1 cm3 = 1 mL
1 dm3 = 1 L
M
D=
V
Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
Basic Algebra Review
• Whatever you do to one side, you do to the other.
2 + 6 + 6 = 12 + 2
3
3
Density
• An object has a volume of 825 cm3 and a
density of 13.6 g/cm3. Find its mass.
GIVEN:
WORK:
V = 825 cm3
D = 13.6 g/cm3
M=?
M = DV
M
D
V
M = (13.6 g/cm3)(825cm3)
M = 11,220g  11,200 g
Density
• A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
WORK:
D = 0.87 g/mL
V=?
M = 25 g
V=M
D
M
D
V
V=
25 g
0.87 g/mL
V = 28.7356  29 mL
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 Prefix Conversions
532 m
NUMBER
UNIT
0.532 km
= _______
=NUMBER
UNIT
SI Unit Conversions
• King __doofus can milk many newts.
• k__ d c m m n
• kilo, deci, centi, milli, micro, nano
• What’s yours?
Dimensional Analysis
• Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top 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
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 1 in
2.54 cm
= 3.2 in
Dimensional Analysis
• How many milliliters are in 1.00 quart of
milk? (1L = 1.057 qt)
qt
mL
1.00 qt

1L
1000 mL
1.057 qt
1L
= 946 mL
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)
cm3
lb
1.5 lb 1 kg 1000 g 1 cm3
2.2 lb
1 kg
19.3 g
= 35 cm3
Dimensional Analysis
• Convert 60.0 km/hr into m/sec
60.0 km1000
1 hr
m 1 hr
1 min
1 km 60 min 60 sec
= 16.7 m/sec
SI Prefix Conversions
1) 20 cm =
0.2
______________
m
32
2) 0.032 L = ______________
mL
3) 45 m =
45,000
____ mm
0.0805
4) 805 dm = ______________
km
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 ug 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 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.