Scientific Notation pt1
Summary
TLDRToday's lesson focuses on scientific notation, a method to express extremely large or small numbers concisely. The video explains the importance of Avagadro's number in chemistry and how scientific notation simplifies its representation. The key rules are highlighted: move the decimal point to have one non-zero digit to the left, and the exponent indicates the number of places moved. Examples demonstrate converting large and small numbers into scientific notation, emphasizing the coefficient and exponent. The video concludes with a preview of upcoming content on performing calculations using scientific notation.
Takeaways
- 🔢 Scientific notation is used to express very large or very small numbers in a compact form.
- 📏 The first rule of scientific notation is to move the decimal point so that there is only one non-zero digit to the left of the decimal.
- ✏️ Rule number two states that the exponent in scientific notation represents the number of places the decimal point has been moved.
- 🔑 The general form of a number in scientific notation is a coefficient multiplied by 10 raised to the power of an exponent.
- 🔄 For large numbers, the exponent is positive, and for small numbers, the exponent is negative.
- 🔎 Significant figures (sigfigs) can affect how you determine the coefficient in scientific notation.
- 🧮 Avogadro's number, a critical number in chemistry, is often expressed in scientific notation due to its large size.
- 📉 When dealing with small numbers, the decimal point is moved to the right, resulting in a negative exponent.
- 🔠 The coefficient in scientific notation is the non-zero digits left after adjusting the decimal point according to the first rule.
- 📚 In the next video, calculations using scientific notation will be discussed, often involving the use of a calculator.
Q & A
What is the purpose of scientific notation?
-Scientific notation is used to condense very large or very small decimal numbers into a more manageable form for calculations and representation.
What is Avogadro's number and why is it important in chemistry?
-Avogadro's number is the number of particles in a mole of a substance, which is approximately 6.02 × 10^23. It is crucial in chemistry as it helps in understanding the relationships between the macroscopic and microscopic properties of substances.
What is the first rule for expressing a number in scientific notation?
-The first rule is to move the decimal point so that there is only one non-zero digit to the left of the decimal point.
Can you explain the role of the exponent in scientific notation?
-The exponent in scientific notation indicates the number of places the decimal point has been moved. It is a power of 10 and is positive if the decimal point is moved to the left and negative if it is moved to the right.
What is meant by the coefficient in scientific notation?
-The coefficient in scientific notation is the non-zero digit(s) that remain after the decimal point has been moved according to the first rule. It is multiplied by 10 raised to the power of the exponent.
How do you determine if the exponent should be positive or negative when expressing a number in scientific notation?
-The exponent is positive if the original number is greater than 1 and the decimal point is moved to the left. It is negative if the original number is less than 1 and the decimal point is moved to the right.
What happens to the exponent in scientific notation when dealing with very small numbers?
-For very small numbers, the exponent in scientific notation is negative, reflecting the movement of the decimal point to the right to satisfy the first rule.
How can you convert a number from scientific notation back to its standard form?
-To convert from scientific notation to standard form, move the decimal point to the right for positive exponents and to the left for negative exponents by the number of places indicated by the exponent, filling in zeros where necessary.
Why is it important to know how to perform calculations with scientific notation even if a calculator can do it?
-Understanding calculations with scientific notation is important because there are instances where a calculator may not be available, or it is necessary to understand the underlying mathematics for educational or professional purposes.
What is the significance of significant figures in scientific notation?
-Significant figures are crucial in scientific notation as they determine the precision of the measurement. When expressing a number in scientific notation, only the significant figures are retained, and trailing zeros after the decimal point are not counted.
Outlines
🔬 Introduction to Scientific Notation
This paragraph introduces scientific notation, a method used to express very large or very small numbers in a more manageable form. The importance of Avogadro's number in chemistry is highlighted, emphasizing its significance in calculations involving moles. The speaker explains the need for a system like scientific notation due to the impracticality of inputting extremely long numbers into calculators. The rules for scientific notation are outlined: the decimal must be moved to the right of the first non-zero digit, and the exponent indicates the number of places the decimal has been moved. The speaker also discusses the concept of the coefficient in scientific notation, which is the number that remains after the decimal has been adjusted. The process of converting a large number, such as Avogadro's number, into scientific notation is demonstrated, with a focus on the movement of the decimal point and the calculation of the exponent.
📉 Scientific Notation for Small Numbers
The second paragraph continues the discussion on scientific notation, this time focusing on its application to small numbers. The speaker explains that the same principles apply: moving the decimal point to the right of the first non-zero digit and counting the number of places moved to determine the exponent. Since the number is small, the exponent will be negative. The speaker provides an example of converting a small number into scientific notation, emphasizing the importance of counting the correct number of decimal places moved. The paragraph also touches on the process of expanding scientific notation back into standard form, illustrating this with examples. The speaker clarifies that when expanding, one should fill in any empty spaces with zeros and provides a method to check the accuracy of the expanded form by converting it back into scientific notation. The paragraph concludes with a teaser for the next video, which will cover calculations involving scientific notation, hinting that while calculators can handle most calculations, understanding the manual process is still valuable.
Mindmap
Keywords
💡Scientific Notation
💡Avogadro's Number
💡Coefficient
💡Exponent
💡Decimal Point Movement
💡Significant Figures
💡Expansion
💡Calculations
💡Mole
💡Placeholder Zeros
Highlights
Scientific notation is used to condense large or very small decimal numbers.
Avogadro's number is a crucial number in chemistry, representing the number of particles in a mole.
Large numbers in scientific notation require the decimal to be moved so only one non-zero digit is to the left of the decimal point.
The exponent in scientific notation indicates the number of decimal places moved.
The coefficient is the part of the number left after collapsing it down to one non-zero digit to the left of the decimal.
For large numbers, the exponent is positive when the decimal is moved to the left.
For small numbers, the exponent is negative when the decimal is moved to the right.
Avogadro's number in scientific notation is 6.02 x 10^23.
When dealing with small numbers, the process of converting to scientific notation involves moving the decimal to the right and using a negative exponent.
The process of converting a number from scientific notation to standard form involves moving the decimal in the opposite direction of the exponent.
Empty spaces in standard form notation are filled with zeros when converting from scientific notation.
Checking your work by converting the number back to scientific notation ensures accuracy.
Calculators are typically used for calculations involving scientific notation, but it's important to understand the manual process.
The next video will cover calculations with scientific notation.
Transcripts
hey kiddos today we're going to talk
about scientific notation now what
scientific notation is for is that we
have to have some way to sort of
condense down an abnormally large or
really small decimal number um so for
instance this number is one of the most
important numbers in all of chemistry
it's avagadro's number this is how many
particles are in a mole of something
that doesn't mean anything at all to you
now but it will um in a will in a few
weeks or a month or whatever um so this
number is really important now in a lot
of calculators you wouldn't even be able
to put this number in as it is because
there's not 20s something digits worth
of number space to type in the numbers
so we need some way to express large
numbers and we'll see here in a second
really small numbers um in a way that
will make a little bit more sense um and
so that's what we're going to do in this
video is show you how to put things in a
scientific notation um and and what
scientific notation means then in our
next video we'll talk about how to do
calculations with it
all right so rule number one for putting
a number a big number or a small number
we'll see here in a minute um into
scientific notation is that we need the
decimal to be moved so that we only have
one nonzero digit left of the decimal
place if you have any more than one
nonzero digit left of the decimal um
then that means that you're not in
scientific notation so you're going to
have to do something to put everything
back into scientific notation so what
that means is that we have a decimal
place here right okay that's unspoken
decimal we know it's there and we need
to move it until it's here so that
that's rule number one I'm not going to
do that just yet because I want you to
see what rule number two is first and
then we'll put everything into the
correct setup okay so rule number two
says that my exponent is going to be the
number of spaces um that we move the
decimal and you might be saying to
yourself what do you mean by exponent
okay so every scientific notation number
has the same general form so there's a
Time
10 raised to some exponential power and
the exponential power is what rule two
applies to however many spaces I move
the decimal that's going to become my
exponent okay so that's the exponential
part of it the other part of the number
is called the coefficient and that's
essentially whatever is left after you
collapse the number back down that that
how much you leave might be dependent on
significant figures or like in the case
that we're going to do here might be
just dependent on hey we're going to cut
it off here and everything else was
zeros and therefore placeholders and so
I'm not as worried about those okay so
let's go ahead and do this then and then
put this number into scientific notation
so we're going to count our
spaces we've got this is where the
decimal is and I'm going to probably
speed up um the counting a little bit
because it's boring to watch me do it
[Music]
so okay so that took us 23 spaces I'm
going to write that down just so that I
don't forget it okay so what that means
is that when I'm going to put my stuff
in scientific notation I automatically
know that my exponent is 23 now it could
be a negative or a
positive um and so there's a couple of
ways to remember essentially if you move
the decimal place to the left you're
going to have a positive number if you
move the decimal place to the right to
obey rule one then that gives you a
negative EXP exponent I always find that
really hard to remember I don't know why
I mean know I probably learned this
stuff 30 something years ago so what
always makes more sense in my brain to
remember is that if it's a big number
like this is then that's a positive
exponents for a really small number like
the next one I'll show you then that's a
negative exponent okay so that takes
care of the exponential part of the
exponential or scientific notation so
what about the rest of it well in this
case I don't really know anything about
my sigfigs so I'm just going to take the
nonzero digits there and I'm I'm going
to count that so
6.02 3 * 10 23rd that's what you're
going to use for avagadro's number in a
wide variety of calculations all right
so we worked a really big number what do
we do with a small number well the same
rules apply I'm going to want one
nonzero to the left of the decimal so
that means my decimal is here now and
I'm going to want it to be right here
okay so I've got to move and count that
many spaces the number of spaces that I
count that's what's going to be my
exponent um and then since I've got a
small number and since I'm moving the
decimal to the right this time my
exponent is going to be negative instead
of the positive that we had before so
real quick just so that I don't forget
anything in the process of doing it I'm
going to go ahead and write down my
times 10 um I can already sort of tell
what my coefficient is but I'm just
going to wait until I count and then
we'll walk through that once we get
there so let's count the numbers now I
sort of divided this out where your
commas would be so that's going to make
it a little bit easier but again I'm
going to go ahead and count them so
it'll be SP sped up a little
okay so we had
34 and so my exponent here is going to
be 34 I move 34 spaces I move the
decimal to the right so therefore it's a
negative also remember it's a small
number so it's going to be a negative
and then we're going to write down what
is left remember that my new decimal is
right here okay so that becomes 6 point
um actually I wrote that number down
wrong that should be
6.62607004 expand them back out just to
make sure that you're clear on that then
in the next video we'll talk about how
to do the calculation part of it okay so
some real quick examples just to make
sure that we're all on board and can do
this so decimal point is here one two
three four spaces so that's going to
give me time 10 to the
4th and then I've got
2.24 * 10 4th okay pretty
straightforward and this case and
remember I move to the left in this case
I'm going to move to the right 1 2 3 4
five remember I have to get this number
to the left of the decimal so that means
I'm left with 6.3 I moved at five
spaces and I moved it to the right which
means it's got a negative in front of it
okay so how about these These are
already in scientific notation so then
what do I do with them then um typically
speaking what you would be asked to do
is probably to expand them back out into
to normal notation in other words
without the times 10 so how does that
work well here it it's pretty
straightforward you go the opposite way
that you did to put it into scientific
notation if I put it into scientific
notation this way then to undo it I go
back the other way so what that means is
if I go left to get a positive exponent
then when I'm expanding a positive
exponent I take the decimal and go back
right and so that's exactly what we're
going to do here I'm going to go one two
three space is right so that would give
me
929 and then you're like well there was
nothing there what do I do well any
empty spaces there you fill in with a
zero okay and how do you know that you
got the right answer well check it put
it back in scientific notation make sure
you got the same number if I move the
decimal here one two three spaces to the
right I get 9.29 * 10 the 3 that's
exactly what I should get so for the
last one again you go the opposite
direction if I go to the right to get a
negative number then I go back to the
left when I have a negative number and
I'm trying to expand it out so in that
case that means I'm going to go one two
three four
spaces okay again what do I do with
those empty spots well you're going to
fill those in with zeros okay and I'm
going to clean that up so you can
actually see it
00178 would be my correct answer now
typically speaking you would sort of put
that other zero there just to let you
know that the decimals there that's not
absolutely necessary and I certainly
wouldn't Mark you wrong for that and
that zero does not count as one of your
spaces remember you're counting the
spaces to get to the correct decimal all
right guys next video we will talk about
how do we do calculations with
scientific notation although I'll tell
you the secret right now most of the
time you're just going to put them in
your calculator and let it do all the
work but you should still know how to do
it um because there are some occasions
when you won't have it thanks kiddos
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