AP Chem Video 1.2 Measurement, metric system, and conversions
Summary
TLDRThis educational video script delves into the fundamentals of the International System of Units (SI), focusing on base units and the significance of metric prefixes. It explains scientific notation for handling large and small numbers, emphasizing the importance of exponents. The script introduces common metric prefixes and their practical applications in chemistry, providing examples to illustrate the appropriate use of units for different measurements. It also guides viewers through the process of unit conversion using dimensional analysis, with step-by-step examples that demonstrate converting between grams and kilograms, meters and centimeters, and picometers to millimeters.
Takeaways
- 🔍 The script discusses the International System of Units (SI) and focuses on measurement, emphasizing the importance of base units and metric prefixes.
- 📏 Base units in the metric system are those without prefixes, such as meters for length, grams for mass, and seconds for time.
- 🔢 Scientific notation is introduced as a method to write very large or very small numbers, using positive exponents for large numbers and negative exponents for small ones.
- 🌐 Examples given include writing seven billion people as 7 × 10^9 and the diameter of an atom as 1 × 10^-10 meters.
- 📋 The script provides a list of metric prefixes, highlighting the most common ones used in chemistry, such as kilo, centi, milli, micro, and nano.
- 📏 The prefix 'kilo' means 10^3 (thousand), and a kilometer is used as an example of a unit that represents a large distance.
- 📏 The prefix 'centi' means 10^-2 (hundredth), and a centimeter is described as approximately the width of a finger.
- 📏 'Milli' and 'micro' are explained with examples like a millimeter being the thickness of a dime and a red blood cell being about 10 micrometers.
- 🔬 The script explains how to choose appropriate units for different measurements, such as using kilograms for the mass of an airplane and milligrams for the mass of an ant.
- 🔄 The process of dimensional analysis is introduced for unit conversions, demonstrating how to convert between grams and kilograms, and from picometers to millimeters.
- 📘 The script concludes with an example problem that involves multiple steps of conversion, illustrating the use of scientific notation and unit cancellation in calculations.
Q & A
What are base units in the metric system?
-Base units in the metric system are units that do not have prefixes. They are used as the fundamental units of measurement for quantities such as mass, length, and time.
Why is scientific notation important in measurement?
-Scientific notation is important in measurement because it provides a convenient way to express both very large and very small numbers, making it easier to write and understand quantities that would otherwise require many zeros.
How is the number of people in the world expressed in scientific notation?
-The number of people in the world, which is around seven billion, is expressed in scientific notation as 7 x 10^9 people.
What is the difference between large and small numbers in scientific notation?
-Large numbers in scientific notation have positive exponents, while small numbers have negative exponents. This reflects the scale of the number being represented.
What is the diameter of an atom in scientific notation?
-The diameter of an atom is approximately 1 x 10^-10 meters, which is a very small number, hence the negative exponent.
Why do we use metric prefixes?
-We use metric prefixes to correlate with the size of what we are measuring, allowing us to express quantities in a more manageable form without having to write out many zeros.
What is the most common prefix used for measuring the distance from North High School to Fargodome?
-The most common prefix used for measuring the distance from North High School to Fargodome is 'kilo', as a kilometer is approximately the distance between these two places.
How many micrometers is a red blood cell in diameter?
-A red blood cell is about 10 micrometers in diameter from edge to edge.
What is the relationship between a nanometer and a micrometer?
-A nanometer is a thousand times smaller than a micrometer, with one nanometer being 10^-9 meters and one micrometer being 10^-6 meters.
How can you determine the most reasonable unit of measure for an object?
-To determine the most reasonable unit of measure for an object, consider the size of the object relative to common objects and the metric prefixes that correspond to that scale.
What is dimensional analysis and how is it used in conversions?
-Dimensional analysis is a process used in conversions where you set up ratios of equivalent units to change a measurement from one unit to another. It involves using conversion factors to cancel out the original unit and replace it with the desired unit.
How many centimeters are in a meter?
-There are 100 centimeters in a meter, which is represented as 1 meter = 100 centimeters.
How do you convert from Pico meters to millimeters?
-To convert from Pico meters to millimeters, you first convert Pico meters to meters, knowing that there are 10^12 Pico meters in a meter, and then convert meters to millimeters, knowing that there are 1000 millimeters in a meter.
Outlines
📏 Introduction to SI Units and Scientific Notation
This paragraph introduces the concept of SI units, focusing on base units that do not have prefixes. It explains the importance of scientific notation for handling very large or very small numbers. Large numbers are represented with positive exponents, while small numbers use negative exponents. Examples given include the world's population in billions and the diameter of an atom. The paragraph also emphasizes the need to understand metric prefixes and their relation to scientific notation, especially the exponents, which are crucial for measurements in chemistry.
🔍 Understanding Metric Prefixes and Examples of Measurement
The paragraph delves into the metric system's prefixes, explaining their significance and providing examples of their use in measurement. It discusses common prefixes such as kilo, centi, milli, micro, and nano, and how they relate to everyday objects like the width of a finger, the thickness of a dime, and the diameter of a buckyball. The paragraph also includes a practical exercise where viewers are encouraged to determine appropriate units of measurement for various scenarios, such as the mass of an airplane or the width of a human hair, and to practice ordering prefixes from smallest to largest based on their exponent values.
📐 Dimensional Analysis and Unit Conversions
This paragraph introduces dimensional analysis as a method for converting units. It walks through the process of converting grams to kilograms, meters to centimeters, and picometers to millimeters. The paragraph emphasizes the importance of understanding which unit is larger and using conversion factors to change from one unit to another. It demonstrates how to set up conversion equations, cancel out units, and perform the necessary calculations to arrive at the correct answer. The examples provided illustrate the practical application of dimensional analysis in converting between different units of measurement.
Mindmap
Keywords
💡SI units
💡Base units
💡Metric system
💡Scientific notation
💡Metric prefixes
💡Dimensional analysis
💡Exponents
💡Conversion factors
💡Pico meter
💡Mega
💡Nano
Highlights
Introduction to SI units and base units without prefixes.
Explanation of scientific notation for large and small numbers.
Example of writing seven billion in scientific notation.
The use of scientific notation for the diameter of an atom.
Metric prefixes and their importance in scientific measurements.
Memorization tips for common metric prefixes in chemistry.
Comparison of units for measuring the mass of an airplane.
Discussion on the width of a finger and its measurement in centimeters.
Understanding the scale of micrometers and nanometers.
Practical examples of using metric prefixes for everyday objects.
Guidance on selecting appropriate units for different measurements.
Ordering of metric prefixes from smallest to largest.
Conversion of units using dimensional analysis.
Conversion from grams to kilograms with a step-by-step example.
Conversion from meters to centimeters using dimensional analysis.
Complex conversion from picometers to millimeters explained.
Use of scientific notation in conversion processes.
Final thoughts on the importance of understanding and applying metric units and scientific notation.
Transcripts
[Music]
all right a brief recap we talked about
the SI units and here we see that there
are several listed for mass length time
etc we're going to talk more
specifically today about measurement now
base units are the ones that do not have
prefixes and here are some examples
notice if there's just the unit by
itself nothing in front of it base units
are prefect there are units without
prefixes we do in the metric system add
prefixes quite frequently to correlate
with how big or small whatever it is
that we're measuring one thing that you
do need to be familiar with here is how
to write numbers in scientific notation
I would have soom that you guys can do
this so big numbers are gonna have
positive exponents and this is how
scientific notation would look the
number of people know in the world I
think is around what seven billion or so
give or take so in this case we would
write 7 times 10 to the nine people
that's equivalent to seven billion which
is written out like this in the long
form so notice that the decimal point
was moved nine places to the left and
that's where we end up with this
exponent of nine now small numbers are
gonna have negative exponents the
diameter of an atom
obviously atoms are going really tiny so
this is very very approximate but the
diameter of an atom is about one times
10 to the negative 10 meters obviously
it's a tiny number is what would look
like one two three four six seven eight
nine okay so it's not very convenient to
write a number with that many zeros and
that's the reason we use scientific
notations for convenience here are the
metric prefixes if you're unfamiliar
with this or don't have this chart shown
in a convenient place you might want to
jot these prefixes down
and pay attention to this part the
scientific notation
specifically the exponents that's what
we are going to need to pay attention to
do you need to know every single one of
these absolutely not there are some of
the more common in chemistry here the
ones that are most important for us that
you should have memorized
starting with kilo up at the top 10 to
the third
okay just to give you from a reference a
kilometer is a distance from North High
School to the fargodome centi is next
here ten to the negative one one
centimeter is about the width of finger
may be this one may be depends on how
big your fingers are but approximately
the width of my little finger is a
centimeter a millimeter is the thickness
of a dime so it's really not very thick
now micrometers it starts getting to
things that are too small to see with
the naked eye and I don't have an
example something that is 1 micrometer
but a red blood cell is about from edge
to edge about 10 micrometers this is the
symbol for micro it's called Greek
letter mu now Nano is a thousand times
smaller than a micrometer so it goes
from 10 to the negative 6 10 to the
negative 9 one nanometer is
approximately the diameter of one
buckyball which is a carbon molecule it
has 60 atoms in a spherical shape again
here here's a list showing those
prefixes if you don't know them jot them
down now try these out what do you think
would be a reasonable unit of measure
for these we're not gonna do every
example here we'll just pick a few so
the mass of an airplane okay we use
grams to measure airplanes one gram is
about the mass of one paperclip would it
be reasonable to measure that in grams
no it'll probably be reasonable to
measure it in Megan's mega grams is a
million grams that's what I would use
the width of your finger we already
discussed that's a centimeter day I'm
gonna have a piece of hair micrometers
or nanometers
it's about 50 micrometres how about this
one the mass of an ant okay so one
paperclip is one gram so I would
probably use centigrams or probably
milligrams so that's a few examples
please try the rest on your own what
about this example if we were to place
these in order from smallest to largest
look at these prefixes and tell me which
one of these is the smallest okay I see
an example okay remember that Nano is 10
to the negative 9 okay so the smallest
one would be one nanometer okay after
that I'm looking for another one that's
really small Micro is 10 to the negative
6 ok let's look at these other examples
we finished that one now this has no
prefix so that's the base unit
centimeter is to the negative 1 now tear
tear meters that's big very big 10 to
the 12th it's a trillion and kilometers
here is 10 to the 3rd so you can just go
based on these exponents from here we
would go to meters 10 to the 0
oops I forgot one there will be
centimeters here okay so we've checked
this one off this one off then it will
be kilometers and then from there will
be of course a tera meter wow that's a
really long distance now here are some
example problems if we're going to do
conversions and this is where we're
going to use a process called
dimensional analysis so here we have
converting from grams to kilograms grams
to kilograms so kilogram gram how many
of these are equal to each other well
this one wants you to think of which one
of these is bigger is a kilogram bigger
or a gram bigger while the kilogram is
bigger kilo is 10 to the third 10 to the
third you could write that that's good
or if you want to write it out of
scientific notation you could write it
as a thousand grams okay so this is what
we're gonna do we're gonna take our
given value which is this one right here
456 and we're going to a calculation
we're gonna stick a 1 underneath here
what we're doing here is we're going to
do a conversion the mathematical
operation I'm using right here is
multiplying so we multiplying the
numbers in the top divided by the
numbers in the bottom whatever unit I
have here I'm gonna write that unit here
okay then I'm gonna look at this
conversion I need to pick the one that
has grams in it I'm gonna use this one a
thousand grams I'm gonna write that next
to it one thousand grams and on the top
I'm gonna write one kilogram the reason
on this is that if I have grams in the
top and grams in the bottom they will
cancel out so this is how I convert I'll
take 450 six times one divided by one
times a thousand and I end up with point
four five six my unit now is kilograms
now I want you to ask yourself this
question does that make sense there's
four hundred and fifty six grams is that
equal to point four five six kilograms
from our kilogram is one kilogram for
every thousand grams it makes perfect
sense same idea here we're going to set
up our work like this put our given to
point one meters we're gonna put meters
on the bottom you can put a 1 here if
you wish it's not required we're
converting it to centimeters we need to
think about what's the conversion now
this is a base unit it has no prefix so
between meters and centimeters ask
yourself which one of these is bigger is
a centimeter bigger or is it meter
bigger meters bigger I'm gonna say one
big bigger meter so how many centimeters
are in that centi means a hundreth so
that means there are 100 centimeters in
one meter I'm gonna match them up now
meters in the bottom put the one they're
centimeters is in the top
put 100 there meters will cancel and
then we're gonna multiply two point one
times 100 so it's 210 centimeters is our
final answer here this last example
they've chosen for you is a little bit
more difficult notice that we're
converting from Pico meters to
millimeters there they both have a
prefix so I'm gonna do two conversions
picometers two meters meters two
millimeters all right which one of these
is bigger Pico or a regular meter one
meter is a lot bigger and so how many
Pico meters are in one meter there's a
lot of them there's 10 to the 12th
there's a billion Pico meters in 1 meter
the next conversion I'm gonna use go
through meters to millimeters which one
of these is bigger a meter which is
about the height of a child or a
millimeter which is the thickness of a
dime well obviously a meters larger and
there are a thousand millimeters in one
meter okay so let's begin again take our
given here seventy six point two Pico
meters and that's how we have to do it
we have to take this unit p.m. we have
to put that on the bottom so it's going
to cancel we go look at our conversions
10 to the twelfth goes next to the Pico
meter unit and one meter goes on the top
now this cancels out Pico meters cancels
up but I'm not done because I wasn't
asked how many meters it is I was asked
to convert it to millimeters so I didn't
do another step yes I organize my work
whatever unit I have here on the top I
want to put that unit on the bottom
because I want it to go away
I've already used this conversion factor
nine to use this conversion factor one
meter is equal to a thousand millimeters
so now meters cancels and what do I have
left I'm going to look at my units here
so this is really something that you
might want to use your calculator for it
it depends it's just personal preference
so I'm gonna do something simplify it
for myself
here this I'm gonna convert to
scientific notation which is really 10
to the third
okay so I have seventy six point two
times ten to the third and dividing it
by ten to the twelfth
the unit is millimeters ten to the
twelfth goes into ten to the third
remember if you're dividing by numbers
in scientific notation you're
subtracting their exponents so it's
really seventy six point two times ten
to the negative nine millimeters I'm
actually going to leave it in that form
for now and we'll talk about how to
convert that to a more proper form
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