Download 3.5 x 10 3

Scientific Measurement
Ch. 3
Scientific Notation
3-1
Qualitative vs. Quantitative
– Qualitative observations – descriptions of
the quality of the object or its physical
appearance
(examples: oval, square, round, cold, hard,
salty)
– Quantitative observations – numbers or
amounts that describe the object
(examples: 3 inches wide, 2.5 grams, 98.6 F)
The room is cold would be a
A) Qualitative observation
B) Quantitative observation
C) Precise observation
D) All of the above
Scientific Notation
• Way to express numbers through the power of 10
• Powers of 10:
100 = 1
101 = 10
102 = 10x10
103 = 10x10x10
• Goal: express large and small numbers
in a single digit
• Example:
– 3500 becomes
– 3.5 x 10 x 10 x10
– 3.5 x 103
Scientific Notation
• Short cut:
– Count the number of
spaces you move left or
right until decimal falls
just after first nonzero
digit
– 3500 to 3.5 is 3 jumps
left
– For each jump left add a
positive exponent on the
10.
– For each jump right add
a negative exponent on
the 10
– So 3500 is now 3.5 x 103
Let’s Try!
•
Convert to scientific
notation:
1. 625
6.25 x 102
2. 8,000,000
8 x 106
3. 0.0075
7.5 x 10-3
•
Convert to normal:
1. 6 x 102
600
2. 5.003 x 103
5003
3. 8.03 x 10-4
0.000803
4. 3.567 x 10-2
0.03567
When converting back to normal, jump the decimal
the opposite way.
-For positive exponent, jump right (make # bigger)
-For negative exponent, jump left (make # smaller)
Scientific Notation when
Multiplying + Dividing
• When multiplying, add • When dividing,
the powers of 10
subtract the powers of
10
• Ex:
12
(4.5 x 1012)(3.0 x 108) • Ex: 4.5 x 10
3.0 x 108
= (4.5 x 3.0) x 1012+8
= 1.5 x 10(12-8)
= 13.5 x 1020
4
21
=
1.5
x
10
= 1.35 X 10
Addition/Subtraction in Scientific
Notation
• Before adding or subtracting in scientific
notation, you need to make the exponents
the same in both numbers.
• (5.40 x 103) + (6.3 x 103)
= (5.40 + 6.3) x 103
= 11.7 x 103
= 1.17 x 104
Let’s Try!
• (4x107) x (2x10-3)
= (4x2) x 107+(-3)
= 8x104
• (6.3x10-2) / (2.1x104)
= (6.3/2.1) x 10-2-4
= 3.0x10-6
• (4.6x103) – (1.8x103)
= (4.6-1.8) x 103
= 2.8x103
Significant Figures +
Uncertainty in Measurements
3-2
Significant Figures
•
•
•
Used for accurate measurements
Meaningful digits are significant figures (sig figs).
Rules:
1.
2.
3.
4.
5.
All nonzero digits are significant (1-9)
Ex: 283.47g ____ # of sig figs
Zeros occurring in the middle are significant
Ex: 56.06g
____ # of sig figs
Zeros to the right (trailing), if there is a decimal point, are
significant
Ex: 73.00g
____ # of sig figs
Zeros to the right (trailing), with NO decimal point, are
NOT significant
Ex: 100g
____ # of sig figs
Zeros to the left (beginning) of the first nonzero digit are
NOT significant
Ex: 0.09g
____ # of sig figs
Let’s Try!
• How many sig figs?
– 0.0672mL
3
– 1.526g
4
– 0.10mg
2
– 607mm
3
– 0100
1
• Round to 2 sig figs:
– 0.0672mL
0.067mL
– 1.526g
1.5g
– 0.10mg
0.10mg
– 536,000
540,000
Rounding:
If > 5 round up
If < 5 stays same
More Sig Figs
(College Prep only, Concept cross out)
• Addition/Subtraction:
– The answer has only
as many decimal
places as the
measurement having
the least # of
decimal places.
– Ex: 190.2g +
65.291g + 12.68g =
267.871g
• Round to tenths
place 267.9g
• Multiplication/Division:
– The answer has only
as many sig figs as
the measurement
with the least # of sig
figs.
– Ex: 13.78g/11.3mL =
1.219469g/mL
• Round to 3 sig
figs 1.22g/mL
(College Prep ONLY)
Addition or Subtraction
The limiting term is the one
with the smallest number of
decimal places to the right.
12.11
8.0
+1.013
21.123
Round off
21.1
(College Prep ONLY)
Multiplying or Dividing
The limiting term is the one
with the fewest number of sig
figs.
12.11 x 18.0 = 217.98
Round off
218
You Try! (College Prep ONLY)
• What is the answer in the correct sig figs?
• 7.55m x 0.34m = 2.567m2
2.6m2
• 74.626m - 28.34m = 46.286m
46.29m
MEASUREMENT in LAB
• Always Estimate the last place.
1 cm
2 cm
1.85 or 1.84 cm
While the last number is uncertain, it is more
accurate than rounding to 1.8 cm
READING A RULER
Accuracy, Precision and Error
• Accuracy is the measure of how close a
measurement comes to the actual or true
value
• Precision is the measure of how close a
series of measurements are to one
another
• Error is the difference between the
accepted value and the experimental
value.
Precision vs Accuracy
• The first bulls-eye has no
precision and no accuracy.
• The second bulls-eye has
precision but no accuracy.
• The third bulls-eye has
precision and accuracy.
In a lab setting, which
outcome is most desirable?
Calculating Percent Error
• Accepted value = correct value based on reliable
references
• Experimental value = value measured in lab.
• Percent error =
[accepted - experimental] x 100
accepted value
• Ex: [100°C – 99.1°C] x 100
100°C
= 0.9% error
Calculator Input (not in notes)
• Find button: EE, EXP, x10, x10n, x10x
(DON’T use 10x or ∧)
• These buttons mean “x10” with one press
• To input (3.2x106) x (6.8x10-3) type:
3.2 EE 6 x 6.8 EE -3
= 21760
• Try (8.99x104) / (6.5x10-23)
8.99 EE 4 / 6.5 EE -23
= 1.383x1027
Calculator Input (not in notes)
• Put calculator in scientific notation:
– Find “mode,” should see “norm or flo, sci, ….”
among other options. Put it in “sci”
– Try 9.5 x 6225
– Should get “5.91375x104” NOT “59137.5”
• Take calculator out of scientific notation:
– Find “mode,” put back in “norm or flo”
– Try 9.5 x 6225 again
– Should get “59137.5” NOT “5.91375x104”
Calculator Input (not in notes –
College Prep only)
• Try:
(6.25x1024) (8.3x103) (1.6x10-5)
(1.92x103) (6.7x1015)
= 6.5x104
• Try:
3.21x10-3 x 2.6x104 x 2.9x106
1.2x10-6
7.9x109
= 2.6x104
International System of Units
3-3
Measurement
• Scientists use the
International System
of Units, or SI.
– Required to keep
measurement
consistent
• Length in meter (m)
• Mass kilogram (kg)
• Volume in cubic
meters (m3)
• Temperature in Kelvin
(K)
• Energy in Joules (J)
DRAW!
Let’s Try Metrics
• 1250 m = _____ km
– 1.25km
• 5.6 kg = _____ g
– 5600g
• 16 cm = _____ mm
– 160mm
• 120 mg = ____ g
– 0.12g
• Use <, >, =
(College Prep only)
5 g ____ 508 mg
5 g > 0.508 g
3.6 m ____ 36 km
3.6 m < 36,000 m
Mass vs. Weight
• Mass is the amount
of matter that makes
up an object.
• Weight is a measure
of the force of gravity
on an object
• Weight changes
based on location,
mass does NOT
change.
Volume
• Volume is the amount of space contained
in an object
• Volume of a box = length x width x height,
with the unit cm3
• V=lxwxh
• Water: 1 cm3 = 1 mL = 1 g = 0.001 L
• Volume of object not box shaped: use
water displacement
Water Displacement
• Ex:
– fill graduated cylinder
with 200mL (cm3) of
water
– Drop in a penny
– Water level increases to
270mL
– How much volume does
the penny have?
270mL – 200mL = 70mL!
Density
3-4
Density
• Density is the amount of matter (mass) compared to
the amount of space (volume) the object occupies.
• Units in g/cm3 or g/mL
• Calculate using formula or wheel
D=m
v
m = D*v
v=m
D
Ex: D = ?
m = 10 g
v = 2 mL
D = 5 g/mL
Mass
Density
Volume
Ex: m = ?
D = 12 g/cm3
v = 2 cm3
m = 24 g
• Which substance is the
densest?
honey
• Which substance is the
least dense?
lamp oil
Temperature
3-5
Measuring Temperature
• Celsius scale: water freezes at 0°C, boils at
100°C
• Kelvin scale: water freezes at 273K, boils at
373K
• Absolute zero = 0 K = -273 °C
• Conversion:
K = °C + 273
°C = K – 273
• If it is 37 °C, what K is it?
K = 37 °C + 273
= 310K