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Which notation is used to make it easier to work with very large or very small numbers?
Scientific Notation

When looking at a set of results from findings/calculations, what role does Accuracy and Precision play?
They are used to know how far the calculations can be trusted

What is the basic form of an equation in scientific notation?
x * 10^{n}

True or False: Standard scientific notation is the only scientific notation where x lies between 1 and 10.
True

In scientific notation, what does the n in 10^{n} represent?
The number of decimal places the decimal point must be moved to convert the number from scientific to conventional notation.

In scientific notation, what does a negative exponent such as 10^{5} mean?
The negative exponent indicates a number less than 1.

In scientific notation, what does a positive exponent such as 10^{8} mean?
The positive exponent indicates a number greater than 1.

When converting scientific notation to conventional notation, the decimal point must be moved to the ______ if the exponent is negative.
left

When converting scientific notation to conventional notation, the decimal point must be moved to the ______ if the exponent is positive.
right

True or False: When adding or subtracting numbers in scientific notation, it does not matter if numbers have different exponent values.
False
7.30 x 10^{15}  4.9 x 10^{14} = ?
4.9 x 10^{14} = 0.49 x 10^{15}
7.30 x 10^{15}  0.49 x 10^{15} = 6.81 x 10^{15}

Describe how to multiply or divide two different numbers in scientific notation without using a calculator.
Division: Divide "x" parts of numbers, subtract exponent on bottom number from exponent on top number.
( 3.6 x 10 ^{19}) / ( 1.2 x 10 ^{14}) = 3.0 x 10 ^{5
}Multiplication: Multiply "x" parts of numbers, add exponent
 (4.5 x 10^{14})(6.0 x 10^{6}) = 27 x 10^{8}

What is a Systematic Error?
The result of gross mistakes (i.e. misreading a ruler); often gives large errors.
(Mars lander that burned up in atmosphere because standard was not converted to metric etc.)

In several measurements of the same quantity, what does a Systematic Error tend to do?
They tend to produce values that are either all higher or all lower than the true value.

What is a Random Error?
Arises from the fact that measurements are estimates.

In several measurements of the same quantity, what does a Random Error tend to do?
These estimates will be tightly clustered around the true value if no systematic errors are also present.

True or False: Accuracy vs. Precision of measurements both involve estimates.
True

In Accuracy vs. Precision of measurements, what is Accuracy?
How close a measurement, or the average of several measurements, is to the true answer.

In Accuracy vs. Precision of measurements, what is Precision?
How exactly or sharply a measurement is reported, or how closely several measurements agree with each other.

Is the following accurate, or precise?
6X7
("" are measurements taken, X is true)
Fair accuracy, poor precision
(A large random error is present)

Is the following accurate, or precise?
6X7
("" are measurements taken, X is true)
Poor accuracy, fair precision
(Random error is less, but a systematic error is also present).

Define Significant Figures.
A measure of the degree of precision in measurements.

True or False: Exact numbers have an finite number of significant figures.
false

What are two kinds of exact numbers?
 1) Counting
 2) Numbers in definitions

True or False: The number of significant figures in measurements is not determined by the measuring device used.
false; it is determined by the measuring device used.

True or False: All nonzero digits are significant.
true

True or False: All zeroes sandwiched between two nonzero digits are insignificant.
false; 7.04 grams has three significant figures.

True or False: All zeroes located at the beginning of a number are significant.
false; they are not significant, 0.00704 kilograms has three significant figures.

True or False: Zeroes at the end of a number and after a decimal point are always significant.
true; 36.00 has four significant figures

True or False: Zeroes at the end of a number and before the decimal point may or may not be significant.
true; 480 may have two or three significant figures. The ambiguity is removed with scientific notation.

True or False: The number of significant figures changes when the units change.
false
0.00704 kg = 7.04 g = 7040 mg
All of these have three significant figures

True or False: It is fine to round off a raw measurement.
false

When making measurements in the laboratory, what is the rule for "rounding"?
Estimate to one tenth the incrementation of the measuring device by "reading between the lines".

Using a ruler, you find that a paper clip is between 2.4 and 2.5 cm in length, and it is about 0.06 cm beyond the 2.4 mark. How long is the paperclip?
How many significant figures are there?
2.46 cm; only three significant figures, with some uncertainty in the last digit.

When multiplying or dividing significant figures, your answer should have only as many significant figures as the least precise of the numbers with which you are working. Why?
There is some uncertainty in the last digit.
0.0 23 x 30.4 = . 70, NOT 0.6992
69.3868 g / 9.14 mL = 7.59 g/mL.
For example, change the last digit of each number by one:
 69.3868 g / 9.14 mL = 7.59 g/mL (7.591)
 69.3867 g / 9.15 mL = 7.58 g/mL (7.583)
 69.3869 g / 9.13 mL = 7.60 g/mL (7.599)
The third digit in the answer changes very little. However, the fourth digit in each case is very different (1 vs. 3 vs. 9).

With adding and subtracting, the _________ determines the number of significant figures in the answer.
position of the decimal point
48.2 + 33.7654 + 24.81 = 106.8
(The 2 in 48.2 is uncertain)
17.59mL – 12.39mL = 5.20mL
(NOT 5.2mL or 5.200mL)

True or False: A number that has been rounded should have the same number of digits to the left of the decimal point, both significant and
not significant, as the original number.
true
16,234.75 rounded to two significant figures is 16,000, not 16.
An exception would be $9.99 rounded to the nearest dollar is $10.00, not $9.00.

What is 16,234.75 rounded to two significant figures?
16,000 (NOT 16).

If the first digit to be eliminated through
rounding is less than 5, round _______.
down
69.485 rounded to the nearest whole number is 69

If the first digit to be eliminated through
rounding is either greater than 5 or is 5 followed by more digits: round ________.
up
Both 69.51 and 69.78 rounded to the nearest whole number give 70 in each case.

If the digit to be rounded off is exactly 5: round ________.
to the nearest even number
69.5 rounds to 70 and 68.5 rounds to 68.

When performing subtraction followed by multiplication or division, how many significant figures will the following equation produce when solved?
(3.79 g  2.99 g)/1.71 mL = 0.80g/1.71 mL = ?
three: 0.47g/mL
Note that the subtraction step determined the number of significant figures.

When performing addition followed by multiplication or division, how many significant figures will the following equation produce when solved?
(4.84 + 7.34)/27.65 = 12.18/27.65 = ?
four: 0.4405, NOT 0.441

What are the basic units of the classical metric system?
 Length: meter (=m)
 Mass: gram (=g)
 Volume: liter (=L)
 Time: second
 Temperature: Celsius (^{o}C) or Kelvin (K)
 Moles

How many inches is 1 meter?
about 39.37 inches

How many grams does a penny weigh?
About 3 grams

How many basic units does 1 kilo represent?
 1,000 basic units
 1 kilogram = 1,000 grams
 1 kilometer = 1,000 meters

What does the prefix centi (c) mean?
 1/100 of the basic unit
 100 centimeters (cm) = 1 meter

What does the prefix milli (m) mean?
 1/1,000 of the basic unit
 1,000 milligrams (mg) = 1 gram
 1,000 millimeters (mm) = 1 meter
 1,000 milliliters (mL) = 1 liter

What does the prefix micro (mc or μ) mean?
 1/1,000,000 of the basic units
 1,000,000 micrograms (mcg or μg) = 1 gram
 1,000,000 microliters (mcL or μL) = 1 liter

What does the prefix nano (n) mean?
 1/1,000,000,000 of the basic unit
 1,000,000,000 nanometers (nm) = 1 meter

What does the acronym in SI units of measurement stand for?
Système International, French, meaning Internation System (of measurements) in English.

What are the SI units of measurement?
Quantity Unit Symbol
 Length meter m
 Mass kilogram kg
 Time second s
 Temp. kelvin K

The SI unit for volume is what?
1 m^{3}

What is most commonly used to measure a unit of volume in SI units of measurement?
The liter (a nonSI unit)
It's most often used because it is more convenient.
1 L = 1 x 10 ^{3 }m ^{3} = 1 cubic decimeter
 1 cubic decimeter = 1 dm^{3}
 1.057 qt = ~1 L

In the lab, how will units of volume most often be measured?
milliliters (mL)

What is the link between units of length and volume?
1 mL = 1 cm^{3} = 1 cc

if 2.54 cm = 1 inch, 11 cm = how many inches?
 (11 cm) (1 in) 11 cm
  x  => 
 1 2.54 cm 2.54 cm
= ~ 4.33 in

7 1/2 inches = how many cm?
 7.5 in 2.54 cm
  x  = 19.05 cm
 1 1

12 inches = 1 foot. 2.5 ft = ? cm = ? m
2.5 ft * 12 in = 30 in = 76.2 cm = 0.762 m

If a car is travelling at 65 miles per hour, how fast is it moving in meters per second?
1 mile = 1.61 km, 60 sec. = 1 min., 60 min. = 1 hour
 (65 miles) (1.61 km) (1000 m) (1 hour)
  x  x  x 
 1 hour 1 mile 1 km 60 min
 (1 min)
  => (65 * 1.61 * 1,000) / (60 * 60)
 60 sec

A sample of iron ore weighs 87.91 grams. If 55.85 grams of this sample is iron, what is the percentage of iron in the sample?
55.85 / 87.91 * 100 = 64.53%

1 square yard (= 1yd^{2}) = ? square feet (=ft^{2})
1 yard = 3 feet, so:
1 yd^{2} = 3 ft^{2} = 9 ft^{2}

1 cubic foot = ? cm^{3} = ? m^{3}
1 foot = 12 inches * 2.54 = 30.48 cm, so:
(30.48)cm^{3} = 28,317 cm^{3} / 100 cm^{3} = 283 m^{3}

What is the most commonly used unit of measurement for density?
NonSI units of g/mL (= g/cm^{3})

A block of unknown material measures 1.5 cm by 2.0 cm by 3.5 cm and weighs 8.5 g. What is its density? Will it float in water?
Density = mass / volume
volume = 1.5 cm x 2.0 cm x 3.5 cm = 10.50 cm ^{3}
mass = 8.5 g
Density = 8.5 g / 10.50 cm ^{3} = 0.81 g/cm ^{3}
 ^{}
 0.81 g/cm^{3} = 0.81 g/mL
Density of water is 1.00 g/mL > 0.81 g/mL
It will float in water.

How do you calculate density?
Density = mass/volume

