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 2.30x10 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 7.211x10 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. 8.72x10 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 1.489x10 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 1.2409x10^-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
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