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
Describe the difference between a qualitative and a quantitative measurement.

Describe the difference between accuracy and precision.

Write a number in scientific notation.

State the appropriate units for measuring length, volume, mass, density, temperature and time in the metric system.

Determine the number of significant figures in a measurement or calculation.

Calculate the percent error in a measurement.

Calculate density given the mass and volume, the mass given the density and volume, and the volume given the density and mass.

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 Scientific Method is a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses and formulating theories that are supported by data.
Observations Hypothesis Experimentation
Theory

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• Collecting data
• Measuring
• Communicating with other scientists

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Measurements are divided into two sets:
Qualitative – a descriptive measurement.
Color, hardness, shininess, physical state.
(non-numerical)
Quantitative – a numerical measurement.
Mass in grams, volume in milliliters, length in meters.

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A tentative explanation that is consistent with the observations (educated guess).
An experiment is then designed to test the hypothesis.
Predict the outcome from the experiments.

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Attempts to explain why something happens.
Has experimental evidence to support the theory.
Observations, data and facts.

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What is the scientific theory?
What is the difference between qualitative and quantitative measurements?
Which of the following are quantitative?
a. The liquid floats on water?
b. The metal is malleable?
c. A liquid has a temperature of 55.6 o C?
How do hypothesis and theories differ?

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Measurements represent quantities.
A quantity is something that has magnitude, size or amount.
All measurements are a number plus a unit (grams, teaspoon, liters).

 Quantity = number + unit
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UNITS MATTER!!

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Use SI units — based on the metric system
Length Meter, m
Mass gram, g
Volume Liter, L
Amount mole
Temperature kelvin, K

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Tera-
Giga-
Mega-
Kilo-
Hecto-
Deka-
Base
Deci-
Centi-
Milli-
Micro-
Nano-
Pico-
1 T (base) = 1 000 000 000 000(base) = 10 12 (base)
1 G (base) = 1 000 000 000 (base) = 10 9 (base)
1 M (base) = 1 000 000 (base) = 10 6 (base)
1 k (base) = 1 000 (base) = 10 3 (base)
1 h (base) = 100 (base) = 10 2 (base)
1 d a(base) = 10 1 (base)
1 ( base ) = 1 (base) meter, gram, liter
1 d (base) = 10 -1 (base)
1 c (base) = 10 -2 (base)
1 m (base) = 10 -3 (base)
1 µ(base) = 1 000 000 (base) = 10 -6 (base)
1 n(base) = 1 000 000 000 (base) = 10 -9 (base)
1 p(base) = 1 000 000 000 000(base) = 10 -12 (base)

15 teragigamegakilohectodeka-
BASE UNIT decicentimillimicronanopico-
Prefix Symbol Factor da
--d c m
 n p
T
G
M k h
10 12
10 9
10 6
10 3
10 2
10 1
10 0
10 -1
10 -2
10 -3
10 -6
10 -9
10 -12

1. 1000 m = 1 ___
2. 0.001 g = 1 ___
3. 0.1 L = 1 ___
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4. 0.01 m = 1 ___
Learning Check a) mm b) km c) dm a) mg b) kg c) dg a) mL b) cL c) dL a) mm b) cm c) dm

1)
20 cm = ______________ m
2) 0.032 L = ______________ mL
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3) 45
 m = ______________ m

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Derived SI Units
Many SI units are combinations of the quantities shown earlier.
Combinations of SI units form derived units.
Derived units are produced by multiplying or dividing standard units.

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Volume
Volume (m 3 ) is the amount of space occupied by an object. length x width x height
Also expressed as cubic centimeter (cm 3 ).
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When measuring volumes in the laboratory a chemist typically uses milliliters (mL).
1 mL = 1 cm 3

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Density
Density – the ratio of mass to volume, or mass divided by volume.
mass
Density = D = volume m v
Density is often expressed in grams/milliliter or g/mL

Density
Density is a characteristic physical property of a substance.
It does not depend on the size of the sample.
As the sample’s mass increases, its volume increases proportionally.
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The ratio of mass to volume is constant.

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Density
Calculating density is pretty straightforward.
You measure the mass of an object by using a balance and then determine the volume.
For a liquid the volume is easily measured using for example a graduated cylinder.

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Density
For a solid the volume can be a little more difficult.
If the object is a regular solid, like a cube, you can measure its three dimensions and calculate the volume.
Volume = length x width x height

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Density
If the object is an irregular solid, like a rock, determining the volume is more difficult.
Archimedes’ Principle – states that the volume of a solid is equal to the volume of water it displaces.

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Density
Put some water in a graduated cylinder and read the volume. Next, put the object in the graduated cylinder and read the volume again.
The difference in volume of the graduated cylinder is the volume of the object.

Volume Displacement
A solid displaces a matching volume of water when the solid is placed in water.
33 mL
27
25 mL

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Learning Check
What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?
1) 0.2 g/cm 3 2) 6 g/cm 3 3) 252 g/cm 3
33 mL
25 mL

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PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3 . What is the mass of 95 mL of Hg in grams?

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PROBLEM: Mercury (Hg) has a density of
13.6 g/cm 3 . What is the mass of 95 mL of Hg?
First, note that
1 cm 3 = 1 mL
Strategy
Use density to calc. mass (g) from volume.
=

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PROBLEM: Mercury (Hg) has a density of
13.6 g/cm 3 . What is the mass of 95 mL of Hg?
=
13.6 g/mL
= mass (g)
95 (ml)

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Learning Check
Osmium is a very dense metal. What is its density in g/cm 3 if 50.00 g of the metal occupies a volume of 2.22cm
3 ?
1) 2.25 g/cm 3
2) 22.5 g/cm 3
3) 111 g/cm 3

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Solution
Placing the mass and volume of the osmium metal into the density setup, we obtain
D = mass = 50.00 g = volume 2.22 cm 3
= 22.522522 g/cm 3 = 22.5 g/cm 3

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Learning Check
The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?
1) 0.614 kg
2) 614 kg
3) 1.25 kg

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Learning Check
The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?
1) 0.614 kg

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Densities of Common Materials
Material Density (g/mL)
Water
Ice
Table sugar
Copper
Gasoline
Mercury
1.00
0.92
1.59
8.92
0.67
13.6

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Textbook: page 42, questions 3 and 5

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Conversion Factors
Conversion factor – Used to convert from one unit to the other. A ratio of units.
Example: the conversion between quarters and dollars:
4 quarters 1 dollar
1 dollar or 4 quarters

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Conversion Factors
Example:
Determine the number of quarters in 12 dollars?
Number of quarters = 12 dollars x conversion factor
4 quarters
1 dollar

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How many minutes are in 2.5 hours ?
Conversion factor
2.5 hr x 60 min
1 hr
= 150 min cancel

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Sample Problem
• You have $7.25 in your pocket in quarters. How many quarters do you have?
7.25 dollars 4 quarters
X
1 dollar
= 29 quarters

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Learning Check
A rattlesnake is 2.44 m long. How long is the snake in cm?
a) 2440 cm b) 244 cm c) 24.4 cm

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Solution
A rattlesnake is 2.44 m long. How long is the snake in cm?
b) 244 cm
2.44 m x 100 cm = 244 cm
1 m

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Textbook: page 59 and 60
Questions: 1, 2, 7,14, 28 and 30
Due:

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Accuracy – refers to how well the measurements agree with the accepted or true value.
Precision – refers to how well a set of measurements agree with each other.

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Three targets with arrows.
How do they compare?
Both accurate and precise
Precise but not accurate
Neither accurate nor precise

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Trial 1
Trial 2
Trial 3
Average
Student 1
27.77 cm
27.30 cm
27.56 cm
27.54 cm
Student 2
27.30 cm
27.60 cm
27.97 cm
27.62 cm
Student 3
27.55 cm
27.55 cm
27.53 cm
27.54 cm
Student 4
27.30 cm
27.29 cm
27.31 cm
27.30 cm
The accepted length of the object is 27.55 cm.
Based on the average values of the measurements which students had the best accuracy?

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Trial 1
Trial 2
Trial 3
Average
Student 1
27.77 cm
27.30 cm
27.56 cm
27.54 cm
Student 2
27.30 cm
27.60 cm
27.97 cm
27.62 cm
Student 3
27.55 cm
27.55 cm
27.53 cm
27.54 cm
Student 4
27.30 cm
27.29 cm
27.31 cm
27.30 cm
The accepted length of the object is 27.55 cm.
Based on the individual trials of the measurements which students had the best precision?

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The accuracy of an individual value can be compared with the correct or accepted value by calculating the percent error.
Percent error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.
Value (experimental) – Value (accepted)
Value (accepted)

 Indicates accuracy of a measurement
=


your value given value
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 A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
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=



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Textbook: page 45, question 2

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Significant Figures
Significant figures – a measurement consists of all the digits known with certainty plus one final digit, which is uncertain or estimated.
Significant figures are the number of digits that you report in your final answer of a mathematical problem.

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Significant Figures
Indicates precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
2.31 cm

RULE 1. All non-zero digits (1-9) in a measured number are significant.
RULE 2. Leading zeros in decimal numbers are NOT significant.
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RULE 3. Zeros between non-zero numbers are significant.

RULE 4. Trailing zeros in numbers without decimals are NOT significant.
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RULE 5. Trailing zeros in numbers with decimals are significant

Counting Significant Figures
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RULE 1. All non-zero digits (1-9) in a measured number are significant. Only a zero could indicate that rounding occurred.
38.15 cm
Number of Significant Figures
4
5.6 ft
65.6 lb
122.55 m
2
___
___

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Leading Zeros
RULE 2. Leading zeros in decimal numbers are NOT significant.
Number of Significant Figures
0.008 mm 1
0.0156 oz
0.0042 lb
0.000262 mL
3
____
____

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Sandwiched Zeros
RULE 3. Zeros between nonzero numbers are significant.
50.8 mm
2001 min
0.702 lb
0.00405 m
Number of Significant Figures
3
4
____
____

Trailing Zeros
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RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders.
Number of Significant Figures
25,000 in.
200 yr
48,600 gal
25,005,000 g
2
1
____
____

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Trailing Zeros
RULE 5. Trailing zeros in numbers with decimals are significant.
Number of Significant Figures
3030.0
0.000230340
50.0
25,005,000.0
5
6
3
9

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Learning Check
A. Which answers contain 3 significant figures?
1) 0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1) 0.00307 2) 25.300
3) 2.050 x 10 3

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Learning Check
In which set(s) do both numbers contain the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000

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Learning Check
State the number of significant figures in each of the following:
A. 0.030 m 1 2 3
B. 4.050 L 2 3 4
C. 0.0008 g 1 2 4
D. 3.00 m
E. 2,080,000 bees
1
3
2
5
3
7

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Rule 1: If the first number to be dropped is 5 or greater, drop it and increase the last retained number by 1.
Rule 2: If the first number to be dropped is
Less than 5, drop it and leave the last retained number unchanged.

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Significant Numbers in Calculations
 Please learn how to calculate with significant figures on your own.
 This includes: adding, subtracting, multiplying and dividing.

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Significant Numbers in Calculations
 The number of significant figures you can report in your answer is based on the type of calculation performed.
 Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing

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Adding and Subtracting
The answer must have the same number of decimal places as the measurement with the fewest decimal places.
25.
2 one decimal place
+ 1.
34 two decimal places
26.54
answer 26.5
one decimal place

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Learning Check
In each calculation, round the answer to the correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B. 58.925 - 18.2 =
1) 40.725
2) 40.73
3) 40.7

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Multiplying and Dividing
For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.

Multiplying and Dividing
You calculate the density of an object that has a mass of 3.05 g and a volume of
8.47 mL. The following division on a calculator will give a value of
0.360094451.
Mass 3.05 g
Volume 8.47 mL
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0.360094452 g/mL

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The answer must be rounded to the correct number of significant figures.
The values of the mass and volume used only have 3 significant figures.
Therefore, the answer can only have 3 significant figures.
0.360094452 g/mL 0.360 g/mL

Learning Check
A. 2.19 X 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 =
1) 61.58
2) 62 3) 60
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C. 2.54 X 0.0028
=
0.0105 X 0.060
1) 11.3
2) 11 3) 0.0413

Significant Figures in Conversion Factors
Conversion factors are considered exact numbers. 100 cm/m
Therefore they are not considered when determining the correct number of significant figures.
m
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4 sig. fig. 1 sig. fig. 4 sig. fig.

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Textbook: page 50, questions 1-4

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Please learn scientific notation on your own.

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Proceed to slide 102

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Scientific notation is a way of expressing really big numbers or really small numbers.

Scientific notation – numbers are written in the form M x 10 n , where M is a number greater than or equal to 1 but less than ten and n is a whole number.
Example: 65,000 = 6.5 x 10 4
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When numbers are written in scientific notation, only the significant figures are shown.

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Small numbers are handled in a similar way; the decimal point is moved to the right:
0.00012 = 1.2 x 10 -4
The decimal place is moved 4 places to the right.
There should be only one digit to the left of the decimal place.

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Examples
• Given: 289,800,000
• Use: 2.898 (moved 8 places)
• Answer: 2.898 x 10 8
• Given: 0.000567
• Use: 5.67 (moved 4 places)
• Answer: 5.67 x 10 -4

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To change scientific notation to standard form…
• Simply move the decimal point to the right for positive exponent.
• Move the decimal point to the left for negative exponent.
(Use zeros to fill in places.)

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• Given: 5.093 x 10 6
• Answer: 5,093,000 (moved 6 places to the right)
• Given: 1.976 x 10 -4
• Answer: 0.0001976
(moved 4 places to the left)

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• Express these numbers in
Scientific Notation:
1) 405789
2) 0.003872
3) 3000000000
4) 2
5) 0.478260

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Calculations with Scientific Notation
Addition and Subtraction
These operations can only be performed if the values have the same exponent (n).
If they do not, adjustments must be made to the values so that the exponents are equal.

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Once the exponents are equal, the M coefficients can be added or subtracted.
The exponents of the answer remain the same.
Example:
4.2 x 10 4 + 7.9 x 10 3 kg
One of these figures needs to be changed to make the exponents equal.

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4.2 x 10 4
+ 7.9 x 10 3
4.2 x 10 4
+ 0.79 x 10 4
4.99 x 10 4
Round to correct number of sig. fig. - 2
5.0 x 10 4

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Alternate method:
4.2 x 10 4
+ 7.9 x 10 3
42. x 10 3
+ 7.9 x 10 3
49.9 x 10 3
Round to correct number of sig. fig. - 2
5.0 x 10 4

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Calculations with Scientific Notation
Multiplication and Division
To multiply numbers, you multiply the coefficients (M) and add the exponents
(n).
To divide numbers, you divide the coefficients (M) and subtract the exponents (n).

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Example:
9.25 x 10 -2 x 1.37 x 10 -5 kg
(9.25 x 1.37) x (10 -2 + -5 ) = 12.7 x 10 -7
1.27 x 10 -6

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Example:
5.23 x 10 6 x 7.1 x 10 -2 kg
(5.23 x 7.1) x (10 6-2 ) = 37.133 x 10 4
Round to correct number of sig. fig. - 2
37 x 10 4
3.7 x 10 5

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Example:
8.27 x 10 5 ÷ 3.25 x 10 3 kg
(8.27 ÷ 3.25) x (10 5-3 ) = 2.54 x 10 2

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Example:
5.44 x 10 7 ÷ 8.1 x 10 4 kg
(5.44 ÷ 8.1) x (10 7-4 ) = 0.6716 x 10 3
Round to correct number of sig. fig. - 2
0.67 x 10 3
6.7 x 10 2

 Calculating with Sci. Notation
(5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) =
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Type on your calculator:
5.44
EXP
EE
7 ÷ 8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 6.7 × 10 2 g/mol

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a) (4 x 10 2 cm) x (1 x 10 8 cm) b) (2.1 x 10 -4 kg) x (3.3 x 10 2 kg) c) (6.25 x 10 2 ) ÷ (5.5 x 10 8 ) d) (8.15 x 10 4 ) ÷ (4.39 x 10 1 ) e) (6.02 x 10 23 ) ÷ (1.201 x 10 1 )

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Textbook: page 54, questions 1-4

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Textbook: page 59 and 60
Questions: 16, 21, 35, 36, 38,
39, 43 and 44