AP Chem Video 1.2 Measurement, metric system, and conversions

Summary

This 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

00:00

📏 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.

05:05

🔍 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.

10:09

📐 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.

Keywords

💡SI units

SI units refer to the International System of Units, which is the modern form of the metric system. It is the world's most widely used system of measurement. In the video, SI units are mentioned as the foundational units for mass, length, time, etc., and are essential for scientific measurements and standardization across different fields.

💡Base units

Base units are the fundamental units of measurement in the metric system, such as meters for length, seconds for time, and grams for mass. They are the simplest units without any prefixes. The video emphasizes that base units are crucial for understanding and performing measurements without the need for conversion factors.

💡Metric system

The metric system is a decimal-based system of measurement that is widely used for scientific, commercial, and everyday purposes. The video discusses how the metric system uses prefixes to denote multiples and submultiples of the base units, which is essential for expressing both very large and very small quantities conveniently.

💡Scientific notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically written as the product of a number between 1 and 10 and a power of 10. The video explains how scientific notation is used to simplify the writing of very large (positive exponents) or very small (negative exponents) numbers, such as the world's population or the diameter of an atom.

💡Metric prefixes

Metric prefixes are used in the metric system to denote specific multiples or submultiples of a base unit. The video provides a list of common metric prefixes, such as kilo (10^3), centi (10^-2), and milli (10^-3), and explains their application in measuring different scales, from the width of a finger to the diameter of a red blood cell.

💡Dimensional analysis

Dimensional analysis is a systematic approach to converting between different units of measurement. It involves multiplying the original measurement by a conversion factor to obtain the desired unit. The video demonstrates how dimensional analysis is used to convert units like grams to kilograms and picometers to millimeters, which is crucial for understanding and performing accurate scientific calculations.

💡Exponents

Exponents are used in scientific notation to indicate the power to which a number is raised. In the context of the video, positive exponents indicate large numbers, while negative exponents indicate small numbers. Understanding exponents is key to correctly using scientific notation and metric prefixes.

💡Conversion factors

Conversion factors are ratios used to convert a quantity from one unit to another. The video illustrates how conversion factors are used in dimensional analysis to change units, such as converting grams to kilograms or meters to centimeters. Knowing the appropriate conversion factors is essential for accurate scientific measurements.

💡Pico meter

A picometer is a unit of length in the metric system equal to one trillionth (10^-12) of a meter. The video uses picometers as an example of a very small unit, suitable for measuring extremely small objects like the diameter of a buckyball, a spherical molecule composed of 60 carbon atoms.

💡Mega

Mega is a metric prefix denoting a million (10^6) times a base unit. The video mentions 'mega' in the context of measuring the mass of an airplane, suggesting that 'mega grams' would be a reasonable unit for such a large mass, illustrating the use of prefixes to express large quantities.

💡Nano

Nano is a metric prefix meaning one billionth (10^-9) of a base unit. The video explains that a nanometer is approximately the diameter of a buckyball, highlighting the importance of nanoscale measurements in fields like materials science and nanotechnology.

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