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Master Scientific Notation: Easy Steps to Convert Big & Small Numbers To The Standard Form
Apr 25, 2025
Struggling with large or tiny numbers in math or science class? In this video, I break down scientific notation in a simple, easy-to-understand way. Whether you're in chemistry, physics, or just trying to make sense of your calculator’s “E” or “10^” output, this lesson has you covered.
Chapters:
00:00 Introduction
00:32 Standard Form
01:11 Scientific form
03:44 How to go from scientific notation to standard notation
09:01 How to express numbers in the scientific notation
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0:00
talking about scientific notation right
0:02
scientific notation
0:04
and you're going to use this in
0:06
chemistry you're going to take this in
0:08
like he's going to take this in physics
0:10
and chemistry so you need to learn this
0:11
right so now there are two types of
0:13
numbers actually not two types of
0:15
numbers numbers are written in two types
0:17
of ways right they can be written using
0:19
the scientific notation or they can be
0:22
written using the standard notation we
0:25
are all used to the standard standard is
0:27
what we all do do every day right like
0:30
five that's a standard number right it's
0:33
it's written in the standard form five
0:36
-10
0:37
1,24 that is the standard 2,300 that is
0:41
the standard this is the standard
0:43
notation okay so you have what is called
0:46
a
0:46
standard and this is what we use on a
0:50
day-to-day basis however sometimes
0:53
numbers can be really gigantic for
0:56
example this is like
0:59
12,760,000 right and this is like
1:04
0.00001276 so these numbers are still
1:07
written in the standard form but you can
1:09
turn them into the scientific notation
1:12
so that way they are easier to write
1:14
this is why we use the scientific
1:16
notation because you use the scientific
1:17
notation to deal with numbers that are
1:20
gigantic like this right they can be a
1:23
really big numbers or really small
1:25
numbers
1:28
0.00001276 sometimes you put stuff in
1:29
your calculator right you put like two
1:31
times uh a million or something and then
1:34
you get two and then 10 to the^ of 6 you
1:37
go what is this a lot of people do that
1:39
that's called a scientific notation
1:40
because your calculator knows how to do
1:42
that okay so you can do that with your
1:44
calculator well it's good to know how to
1:46
do it i know with the advent of AI a lot
1:49
of things are going to change but we
1:51
still need to know how to do it because
1:53
the human the human is the one that
1:55
actually creates the prompt to the AI to
1:58
speed our stuff so as a human you still
2:00
need to learn how to do it yes and also
2:02
if we rely everything on AI then we're
2:04
not going to be able to make any
2:06
decisions for oursel and then we're just
2:07
be making bad decisions of the AI yeah
2:11
is useful though the the AI tool is
2:13
everything is about how you use the tool
2:16
you can use the tool to create great
2:18
stuff that's all about how you use it
2:20
people say Tik Tok is not good you can
2:22
use Tik Tok to do whatever you want that
2:23
is positive you can use social media to
2:26
do positive things and so it's not about
2:29
it's what you do with a tool that is bad
2:31
right now what is the scientific
2:34
notation like I say a number that is
2:36
written in the scientific
2:38
notation is expressed as the product of
2:41
a factor and a power of 10 example if
2:45
you have
2:47
3,500,000 you can rewrite this as what
2:50
3.5 * 10 ^ 6 this is called the
2:55
scientific notation so you just wrote
2:57
this number in the scientific notation
3:00
and vice versa right here I have
3:04
04 and if I want to write this in
3:06
scientific notation it gives me what 4 *
3:10
10 ^ 5 so this is called a scientific
3:13
notation he's basically taking a number
3:15
in the standard form that is either
3:17
extremely big or extremely small and
3:20
transforming so that way is easier to
3:23
read this is the whole point about
3:25
scientific notation it makes it easier
3:27
to read and write numbers yeah so do we
3:31
just like count the zeros and that will
3:32
be our power yeah well we're going to
3:35
get to that right right now we're just
3:36
still just talking about the
3:37
introduction and what they look like now
3:39
we're going to talk about how how do you
3:41
express a number in the standard form if
3:44
the number is in a scientific notation
3:46
right for example if I have 2 * 10 the 3
3:50
i want to express this in the standard
3:52
form this is called a scientific
3:54
notation because this is
3:55
written as a product of a factor and a
3:59
power of 10 right this is the factor and
4:02
this is the power of 10 so this is a
4:04
scientific notation so how do I turn
4:06
this into a standard number so what
4:08
would you do it's 2 * 10 3 so how would
4:11
you turn this yet i know when um
4:13
whenever I multiply something by 10 I'm
4:15
adding a zero adding a zero three zero
4:17
so it's or 2 * 1,000 so 2,00 this is 2 *
4:21
1,000 right 2 * 1,000 so this is
4:24
basically
4:26
2,000 so the scientific notation is 2 *
4:30
10^ 3 and the standard notation is 2,00
4:34
right so in this case it'll be easier to
4:37
use the word 2000 in the number 2000
4:39
instead of 2 * 10 ^ 3 right sometimes
4:42
the scientific notation doesn't really
4:44
make sense 2,00 is better than 2 * 10 ^
4:48
3 right if you were to write that okay
4:50
now I have 6.8 * 10 5 so how do I turn
4:54
this into a uh standard number so I'll
4:58
show you how to do that i start with 6.8
5:00
right and then look how many how many u
5:04
zeros do I add to this five five but we
5:07
start with a decimal number right now if
5:09
you're here you're going to go how many
5:11
time i'm going to move it to the right
5:12
this is the key you're going to move the
5:14
decimal to the right how many times one
5:16
more no two five five times right i'm
5:20
going to go one two three four and five
5:25
and then I'm going to add my
5:27
zeros so therefore this gives me what
5:32
68,000 do you see the key here right you
5:35
just won it you're not 68,000 68,000 oh
5:38
yeah 680,000 oo good yeah you got that
5:43
ah I still I'm still in spring break
5:45
yeah mhm you can tell wait never mind
5:48
right so this is 680,000 because I moved
5:52
I'm going to start with the decimal
5:53
number from here this is where I'm going
5:54
to count i'm going to move it to the
5:56
right five times so it's going to go
5:58
from here 1 and two and three and four
6:02
and five so that gives me
6:03
680,000 right now the next number is
6:07
different what is the exponent
6:10
here is it positive or negative so when
6:13
the exponent is negative do I go left or
6:15
do I go right left i'm going to move the
6:19
the uh the zeros to what to the left
6:22
right so again I'm going to start with
6:24
3.25 now watch this now because I'm
6:27
going left because this is negative
6:29
right it's a negative exponent i'm going
6:31
to go left i'm going to count again how
6:33
many times four so I'm going to go one
6:36
and two and three and four right and I'm
6:40
going to have 0 0 here and I'm going to
6:43
put my dot here so this gives me 0
6:47
03 2 5 do you see what just happened
6:51
right so starting from here you're going
6:53
to move it to the left four times it's
6:55
gonna be one two three and four and then
6:59
put your dot here because this is where
7:00
you aim right so 3.25 * 10 -4 is
7:05
basically
7:07
0.325 is easier to write this using the
7:10
scientific notation in my opinion all
7:12
right now what about 4 * 10 2
7:17
anyone what's that going to be i've been
7:19
using four * 10^2 what would that give
7:22
you i got um 100 * 4 4 * 100 which is
7:28
basically 400 right or if you wanted to
7:31
use the other method you start with a
7:32
four here you're going to move it how
7:34
many times one and two this is
7:37
400 right so this is how you go from the
7:42
uh scientific notation to the standard
7:45
well I want us to do a little more on
7:48
the scientific because I know that it
7:50
can be a little bit hard to to figure
7:51
out especially when the numbers are
7:53
negative so let me give you an example
7:55
here and I want you all to to try to
7:56
work it out right so what if I have 7
8:01
08 right * 10 -3 so how would you write
8:06
that 10 7.08 8 * 10 -3
8:11
so what would you do
8:15
so I want you to go from the uh
8:18
scientific notation here to the standard
8:21
using 7.08 yes
8:24
so what are 7.08 okay and then I know I
8:29
would have to move the decimal to the
8:30
left how many times okay so count so one
8:34
two three and then fill this
8:38
board 0708 there you go so this is
8:43
0708 so this is how it's really just
8:45
easy once you understand the the the
8:48
mechanism right you just either move
8:50
left when it's negative right when it's
8:53
positive when you want to go from the
8:55
scientific notation to the what standard
9:00
right now we're going to do the Now
9:02
we're going to go opposite we're going
9:03
to go from the scientific no we're going
9:06
to go We're going to go from the
9:07
standard to the scientific right now
9:10
here's the key here people get confused
9:13
all the time so when you want to go from
9:15
the standard to the scientific you
9:18
always look at the first digit right i
9:20
have what's my first digit here four
9:23
four right so I'm going to start with a
9:25
four because the number next to the four
9:27
are all
9:28
zeros i'm just going to start with a
9:30
four right i'm going to drop everything
9:33
else because the number next to the four
9:34
are all zeros right so then what I do
9:37
from here is I'm going to count how many
9:38
zeros do I have 1 2 3 4 5 and six so
9:43
it's going to be four * 10 to the^ of
9:44
what six
9:46
six really easy right so now the next
9:50
one is where you need to be careful and
9:52
people get confused a lot right so what
9:53
we do with the next one is this when it
9:56
comes to scientific notation so when a
9:58
number you you always go you you start
10:01
with the first digit five right and then
10:03
you put a dot 5.8 this is what you do
10:06
all the time here I did not do that here
10:08
because all the numbers were zero so I
10:10
didn't have to 4.0 is the same as 4 yes
10:14
what my brain is doing right now is
10:16
you're basically just using this decimal
10:18
point mhm so what how I would solve it
10:21
is I would put a decimal point at the
10:24
end and then I would make to I the
10:27
decimal point to be so 5.8 and then how
10:30
many house would be would be the power
10:32
there you go that works for you right
10:33
good so for a scientific notation the
10:36
key here to is is understanding the
10:38
mechanism right it's always the first
10:41
digit after the first digit you put a
10:43
dot plus the number that follows it
10:45
right so 5.8 Eight and then what times
10:49
what 10 two if I put it here so 10 to
10:52
the power how many zeros do I have one
10:55
two and what three three so find 10 to
10:57
the power of three right you see that so
11:01
this is how you going to write that so
11:02
you're going to start with dot here and
11:04
then from the dot you're going to count
11:05
to the end of the to to the to the end
11:08
right it's one two and three now here
11:10
let's do the same thing now this is a
11:12
negative this is a decimal right so
11:15
because it's decimal we're going to go
11:16
left or right this time we're going to
11:18
have a negative exponent right again
11:20
we're going to do the same thing i'm
11:22
going to start with what 7.2 okay I'm
11:25
going to go here 7.2 so it's going to be
11:29
1 and two and how many times did I move
11:33
one and two so we times 10 to the power
11:35
of what two no two -2 right because it's
11:39
a decimal moving a decimal point you're
11:40
moving a decimal point right so this is
11:42
how we do so now let's do some more
11:44
exercise here so what if I have 1 um
11:50
let's say I have uh
11:55
let's do
11:57
0.0 uh
12:00
0 93 so let's do 0.93 and I also want
12:04
you to do
12:05
um
12:09
1,200 and I want you to write this in
12:12
standard uh in the scientific notation
12:14
so what would be
12:17
0.93 do it 9.3 uhhuh
12:22
times what 10 over2 uh I went to the
12:26
right so
12:28
101 you mean yeah 1 because if you move
12:31
you how many times you move only one
12:33
place so it's 9.3 * 101 right what about
12:37
1200
12:39
1.2* two * what 10 10 to the two to the
12:43
count three three right so it's super
12:47
easy you just have to figure out where
12:49
you going you just go left or right all
12:51
right so this is pretty much the
12:53
scientific notation okay and the
12:55
standard notation now we're going to
12:57
work on some problems I'm going to give
12:58
you some problem to work on and then
12:59
we're going to wrap this
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