Scientific Notation and Standard Form Explained with Practice Problems  | How to Pass Chemistry
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In this video you are going to learn how
to write numbers in scientific notation and in standard form. Alright let’s do
this! hello-hello Melissa Maribel here and I help
students like you understand what you just learned in class so you stress less
and you graduate faster. Hit that subscribe button and we’ll pass
chemistry together. On to scientific notation. Scientific notation is just an
easier way to write really small or really large numbers. You will have two
different forms, standard form is just the expanded form of that number or the
number itself and scientific notation is just the condensed form of that same
number. The proper set up for scientific notation, you will always have one
non-zero number followed by a decimal then after that decimal you will have
one or more numbers. Doesn’t matter if it’s 0 or not and that would have been
times 10 to the some sort of exponent. So you’ll see for example we have 2.30×10 to the 4th. That is an example of your proper scientific notation. If
you wanted to then write a really really small number into scientific notation,
remember that all small numbers will have negative exponents when you put
them in scientific notation. So all numbers less than 1 have negative
exponents. Let’s try one. Write 0.0007211 in scientific notation. This is your clue
this is a very small number or it’s less than 1. So it will have a negative
exponent. What we’re going do, take that decimal place and we’re going to
move it all the way to that 7 because that is your first non-zero number. So
moving this over 1, 2, 3, & 4 putting our decimal place there, we know
that we will have a negative 4 as our exponent because that’s how many places
we move to get to that first nonzero number.
So our proper scientific notation is then 7.211×10 to the negative
4th. When we’re writing numbers that are already in scientific notation and going
back to standard form that exponent tells you whether or not
to move to the right or to the left. So if it’s negative you’re actually going
to move to the left and if it’s positive you’re gonna move to the right. 8.72×10 to -3rd we’re gonna write that in standard form. You’ll see that we have a -3 as our exponent so a -3 recall that tells us it’s going to be a
number that is less than one so we’re going to move the decimal place to the
left three. So I’m going to move this over one two and three and my decimal
place is here. I’m going to place a zero wherever I had any missing spaces and
our final answer is 0.00872. When you’re converting
really large numbers into scientific notation large numbers have positive
exponents. All numbers larger than one have positive exponents. For example
let’s write this ridiculously large number into scientific notation. So
clearly this is larger than 1 so we know it will have a positive exponent.
Your decimal place is always after the 0 or always after that last value
since there wasn’t initially a decimal place and we’re going to move this all
the way over to this 9 because that’s our first non-zero number. So I’m going
to just count one, two, three, four, five, six and seven. So our setup will be 9.0 and then following with all of the numbers that we had before times
10 to the positive 7. Seven because we move that decimal place over seven
times. Let’s write 1.489×10 to the 5th in standard form. Remember standard form now, is just the
expanded form of this number. That 5 tells us it’s a very large number. So
from that decimal place we’re going to actually move over to the right five
times. One, two, three, four, five, placing that decimal place here which
really it’s gone. This would have been zero and zero. The reason I say that that
decimal place is gone is because it’s now a really large number and there’s no
need to put a decimal place since there is no numbers following. So this would be
our correct number in standard form. Sometimes you have numbers that look
like they’re in scientific notation but they actually have two numbers in front
of that decimal place and we know that that’s not correct. So how do you change
them back? If you’re trying to move that decimal place to the left, you will add
how many decimal places you’re moving to that exponent. Now if you’re going the
other way if you’re going to the right, you’re actually going to subtract. I know
it’s always the opposite of what you’re thinking or what you’re used to, but
let’s try some. Though this number looks like it’s in scientific notation, it’s
not because remember we have to have one non-zero number in front of that decimal
place but instead we have two. So we have to move this decimal place over one,
whenever you move over one to the left you will add 1 to that exponent. So
instead we have 1.2409×10^-5 because we added a 1 to that exponent. Now we’re trying to move this decimal
place over one. When we move that over once to the right we will subtract this
exponent by one making it a negative four so when we move over to the left
you add and when we move to the right we subtract. Now it’s just you me and these
practice problems. For practice problems with
step-by-step answers, check the description box. Also let me know if you
want to see more “How to pass Chemistry” videos by liking and subscribing. And
leave a comment below letting me know why you want to pass chemistry and I’ll
see you next week.

18 thoughts on “Scientific Notation and Standard Form Explained with Practice Problems | How to Pass Chemistry

  1. Hi Melissa. To answer your question i'm studying chemistry because it's a very interesting subject. All these chemicals get mixed together and BOOM you get a change in colour…explosion…a gas etc. I'm thinking about taking a (BS) degree in chemistry. The thing is i'm not really sure about it because as you already know i have to be very good at maths and calculations. Maths has always been a problem for me. I have to look over and over again to understand something. I know it will cause a huge problem for me specially when it comes to practical chemistry. I'm not even sure if chemistry is the right major for me. I'm so confused and my mind is all over the place. University is such a big step for me and i don't know what to do. Sorry for the very long comment, but i have no one to talk to about this since i'm homeschooled.

  2. Hi Melissa, I am studying Chemistry because I have to take it in High School LOL. I am currently a Junior. Chemistry is not my favorite subject at all-mostly because it's science and math combine- but your videos are the first ones I go to when I feel stuck. They are EXTREMELY helpful! Can you do a video on electron configurations sometime in the future? Would be very much appreciated:)

  3. Thank you so much! I missed some school and have tons of work to catch up on and your channel (especially this video) Is so much help!

  4. Can you do equations with scientific notation with the equation having subtracting an addition or multiplication with addition

  5. MELISSA! I'm taking chemistry this semester and I'm not so good with math. I hope I pass this course using your helpful videos. If I don't pass then I believe Nursing ain't for me. 🙁

  6. Thank you so much! I relied on calculators so much but you make it so easy to learn without using a Calculator Thanks! Do you have a channel on how to convert metric conversions for volume, length, mass and height?

  7. Thank you for this video! My professor is very smart & explained it 5 different ways which confused me. Thankful for your time in putting this together 💕

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