Scientific Notation Practice Problems
100 Comments


I want to give you some practice with scientific
notation so in this video I’m going to do 12 example problems, step by step, so by the
end the steps should be really easy. Here’s our first example, 483 we want to put it into
scientific notation. So where’s the decimal point? Well it’s not written in this number
but we know that it’s right here so I’m going to put it in. Now, to put this in scientific
notation we need to move this decimal place so there is only one digit, one digit that
isn’t 0, to its left okay? So that means I’m going to move the decimal place over two spots
so that it�s right here and I have just one digit and that’s the four that is to the
left of it and then everything else is on the other side. So I could rewrite this number
as 4.83 because I move the decimal place to here. That’s half of it. Now the other half
of scientific notation is that we have 10 with an exponent on it. So what’s the exponent
on 10 going to be in this example? Well I like to think that we start out when the decimal
place is here, we start out with the exponent being 0, decimal place is here and we are
starting out 10 to the 0 and then when I move the decimal place to the left, what I have
right here, the exponent on 10 goes up. Okay? So I started at 10 to the 0 here, move it
one spot and now it’s 10 to the first, move it another spot now it’s 10 to the second.
So the exponent part of my number is going to be 10 to the second because I’m moved this
decimal place two spots to the left and the exponent went up. So 4.83 times 10 to the
second. This number over here is already written in scientific notation so I want to get it
out of scientific notation. I’m starting at 10 to the fifth here and to take a number
out of scientific notation, I want to move the decimal place so that this number on 10,
the exponent, goes back down to 0. Okay? So it’s a 5 right now and I want the exponent
to go down. So take a look at these rules up here. I want to move the decimal place
to the right so that the exponent will go down. So, I have 3.001 and right now I’m at
10 to the fifth so moving it right one spot I’m at 10 to the fourth. Okay? Move it right
another spot, 10 the third, 10 to the second, 10 to the first, 10 to the 0 and here’s my
new decimal place. Now you’ll see that I moved the decimal point beyond where there were
numbers, I ran out of some of these digits and I introduced two new spots. All you got
to do is fill those in with zeros if that happens so when I rewrite my number so it’s
a little bit neater I end up with 300,100 and again all I did was move the decimal place
to the right so that the exponent went down from 5 down to 0. Okay? We want to write this
in scientific notation so I want to move the decimal place so there is one number that
isn’t a 0 to the left of it. So these are all 0’s so I’m going to move past all these
and I’m going to put it right here so I have a 2, that’s not a 0 and it’s to the left of
where the decimal place is going to be. We’ll be moving it to the right which means the
exponent on the 10 is going down. As we said before, if a number isn’t already written
in scientific notation, it starts at 10 to the 0. So when the decimal place is right
here we at 10 to the 0. Now we move it to the right and we’re going to start going lower
than 1 so we can get into the negatives. So we start at 0 then we go to 10 to the negative
first, 10 to the negative second, 10 to the negative third, 10 to the negative fourth,
and the negative fifth, 10 to the negative sixth, 10 to the negative seventh, and our
new decimal spot location is right here so when I rewrite the number. I don’t worry about
any of these 0’s here because they all come before this non-zero digit and then I write
2.3 times 10 to the negative seventh. This number here I want to take it out of scientific
notation so I get 10 to the negative fourth here I’m going to be moving the decimal place
so that this negative fourth comes back up to 0. Now notice this is a negative number
here, some people get confused by this but the negative number in front of 7.6 has nothing
to do with the negative number in the exponent so don’t be confused by this. They are totally
separate. So what I usually do is I just leave this negative sign out until the very end
and I put it back in. Anyway, I’m starting with 7.6. We want this 10 to the negative
fourth to come back up to 0. We want to move up, exponent moving up, so we’ll move the
decimal place to the left. Okay? Starting at 10 to the negative fourth, negative third,
negative second, negative first, 0. I introduced a few new spots and I’ll fill those in with
0’s. The final answer will be 0.00076. Don’t forget that it’s a negative number so we’ll
add that negative sign there and this is what our final answer taken out of scientific notation
looks like. Now here are a couple example problems that are a little bit trickier, sometimes
people get tripped up by some of what’s in here so I’ll go through here step-by-step.
We’ll be taking this number, putting it in to scientific notation. There isn’t a decimal
place written in right now but we know that it should be here so I’ll draw it there now.
I want to move the decimal place so, all the way over here, so that there is this 8 to
the left of it. Everything else is on the other side and since I’ll be moving it to
the left, the exponent on 10 will be going up. We started 10 to the 0 because it’s not
yet in scientific notation, we’re moving up, 10 to the first, 10 to the second, 10 to the
third, 10 the fourth, 10 the fifth, 10 to the sixth, 10 to the seventh. So that’s that
part of it and now I’m going to do 8 and what else? Nothing else, okay? It’s just 8. This
can be confusing because we’re so used to scientific notation always been like 8.113
or 8.865 but we also get rid of these zeros, okay? So if there’s nothing except for zeros
to the right of the decimal place, just leave it out. This is an 8 point anything, we don’t
even write the decimal place in here, okay? It’s just 8 times 10 the seventh. We’ll put
this, we’ll get this out of scientific notation and start with 4.29. I’m at 10 to the negative
first so I want to go up to 10 to the 0. So I want the exponent to go up, this means that
I’ll be moving the decimal place to the left. So 10 to the negative first right here, move
it one spot to the left and now it’s 10 to the 0. So 0.429 so you have to move the decimal
place but sometimes you don’t have to move it very far. -9 times 10 to the fifth, this
is kind of like this one here because we just have one number, no decimal place, nothing
after the decimal place but you know where the decimal place should be. So, we’ll write
it in here like 9 point because that’s where the decimal would be, it’s a negative number,
we’ll leave that negative out until the very end. It doesn’t have any bearing on what we’re
going to be doing with the decimal. So to be getting it out of scientific notation,
we’ll be taking the 10 to the fifth and bumping that exponent back down to zero. To get the
exponent down, we’ll be moving the decimal place to the right here, okay? Starts at 10
to the fifth, 10 to the fourth, 10 to the third, 10 to the second, 10 to the first,
10 to the 0. I introduced a lot of new spaces here, fill those in with zeros, and 900,000
is what I get. Don’t forget to make it negative and that’s the final answer. Here, we’re going
to put it in to scientific notation, again it’s negative, you should leave that until
the very end. I’ll have to put in the decimal because it wasn’t already written here. I’ll
be moving it all the way over here, moving to the left so the exponent on10 is going
to be going up. Starting at 10 to the 0, 10 to the first, 10 to the second, 10 to the
third, 10 to the fourth, 10 to the fifth, 10 to sixth. And the decimal place ends up
right here. Sometimes that confuses people because they’re used to having, they’re used
to getting rid of the zeros on one side of the decimal places like what do I do here
because they’re zeroes here but then there’s this 2, right? Well we keep any zeros that
are between numbers that are not 0’s, okay? So there’s a 1 here and there’s a two here
so we keep all the 0’s that are in between them but then these 0’s here that are all
the way on the right, we will get rid of these. Our final answer’s going to look like 1.002
and that’s negative so we keep these because they’re between the non-zero numbers but then
we get rid of everything there on the right so that’s what that looks like. I got four
more here, if you really have gotten the hang of this, no need to keep watching but little
practice can’t hurt if you’re still feeling a little uncertain. Start here, put in scientific
notation. I’m going to be moving the decimal place in this direction to the right so the
exponent goes down. Starting at 10 to the 0, 10 to the negative first, 10 to the negative
second, 10 to the negative third, 10 to the negative fourth, 10 to the negative fifth,
10 to the negative sixth, 10 to the negative seventh. There’s a 0 here but it’s sandwiched
between these two nonzero digits so don’t worry about it. I totally forgot what the
exponent was -1, -2, -3, -4, -5, -6, -7. Times 10 to the -7, thanks for hanging in there
with me. 3.08 times 10 to the -7. Take this out of scientific notation 9.53, I’m starting
at negative 6. I got to go up to 0 so I’m going to be moving the decimal place left
so the exponent goes up. Negative 6, negative 5, negative 4, negative 3, negative 2, negative
1, 0. Fill in each one of these new spaces with a 0 and I get 0.00000953. Okay, two more!
Put this in to scientific notation, decimal place is here, moving right, exponent goes
down, start at 10 to the 0, 10 to the negative 1, 10 to the negative 2, 10 to the negative
3, 10 to the negative 4, 10 to the negative 5. 5.713, we don’t keep any of the zeroes
here that are on the left hand side, and this is our final answer. Okay and finally we are
going to take this out of scientific notation. Starting at 10 to the second, we want to get
that to 10 to the 0, we want the exponent to go down so I’m going to move the decimal
place to the right. So 10 to the second, 10 to the first, and 10 to the 0: 324.8. Sometimes
questions like this confuse people because they’re used to moving the decimal place beyond
where there are numbers, right? Where you have to like add in 0’s or get rid of 0’s
but sometimes all you have to do is just move the decimal place in between digits like here.
Just because you’re not adding or getting rid of 0’s doesn’t mean you’re doing anything
wrong. Sometimes all you have to do is move the decimal place a couple spots like this,
you don’t introduced or get rid of any zeros, it’s fine. Okay, so that’s how you do the
scientific notation problems, just a few things you got to keep in mind. If you move the decimal
place to the left the exponent on 10 goes up, if you move the decimal place to right
the exponent on 10 goes down. If your number is not yet in scientific notation you start
at 10 to the 0 and if your number is already in scientific notation like these, you want
to move the decimal place to get exponent on 10 either up to 0 or down to 0. So that’s
all you got to do. Now, if you have time please, please, please watch the video called understanding
scientific notation. It’s good to be able to move the decimal place back and forth and
change the exponent on 10. That’s great, it’s an important skill. But it’s just important
to understand the math behind what’s actually going on here so you can do more than just
move the decimal place but you can look at a number like this and really understand what’s
going on. So please, please, please watch that if you have the time but if you don’t,
if this is the only time you have, you’ll be great. This is a really solid foundation
for how to write numbers in scientific notation and how to get numbers out of scientific notation.

100 thoughts on “Scientific Notation Practice Problems

  1. Why would anyone dislike this video 😭😭

    Thank you. Please upload videos based on topics like electro,magnetic radiation , black body radiation and similar topics. 😊

  2. Your videos are a life saver for me right now. I am taking Chemistry for the first time and I am horrible with math. Your videos give me hope that I will survive the class. You make it so clear! Keep up the videos. You are a great teacher! 🙂

  3. How do you know when stop counting, like in 0.000 000 308. How do you know when to stop counting the numbers to get 10 to the -7 power? Someone please help me.

  4. My math teacher suggested this video on Google Classroom for my class to watch. For a math test. Thanks for the help!

  5. You are so helpful Tyler! Even though I'm in Chemistry 221 (Gen. Chem) in the university, I still need this refresher to get through it. It's amazing how these videos of yours can help people in college as well as kids in maybe middle school or high school. You're making a big difference for many people, so thank you!

  6. This is easy! thanks for making it clear lol I wish you were my 8th grade math teacher (we didn't learn this in science and I don't take Chemistry because I'm not in high school yet)

  7. my teacher wants 2.359×10^-6 to be worked out to 1 Significant Figure. would this then equal
    0.2×10^-6?

  8. how to solve this in standard notation (3×10)+(9×1)+(6×0.1)+(7×0.01 men how to solve this thing

  9. Ditto to Jessagrl89's post. Very thankful for these intro videos. Well done! Many of us have not had scientific notation broken down to the most basic, simple concept….ever. After several years of college, heading towards horticulture and taking my first chemistry class. Yup, there is hope.

  10. Can you put in numerical order of your videos. My son is having trouble with this, and he wants to follow from the beginning. We just found you. Thank you.

  11. I can't thank you enough. I was struggling some of my homework and thhis really made me understood. Thanks again

  12. I absolutely love you!! I have no idea what I would do without your videos!! well, probably cry
    ANYWAYS, teachers just HAVE to watch your videos so they can learn how to teach. Again, I love you and you're amazing!!

  13. I cried over the material my Uni gave me because I felt so lost. I watched 2 of your videos and I get it and can do these with ease. THANK YOU! <3

  14. Thank you so much for making these videos I now have confidence in doing scientific notation and I am ready for my test tomorrow THANK YOU!!!

  15. u r js awesome…teacher ..uh made things crystal clear..nw I dnt have any doubts..thnku..its bcz f u ppl DT learning becomes so easier!!!keep it up!!

  16. I have not disliked the video but it kinda irritates me that he puts a decimal point when there was no decimal to begin with which ends up confusing everyone

  17. Hi! May I ask if the no. is 0.7, 26, and 3.70 how can I derive it in scientific notation? Thank You! Btw I like your Videos!!

  18. I'm wondering what whould be scientific notiation with a lot of decimals an integers, example: 1234567890.1234567890

  19. thank you for posting this tyler its so understandable and educational keep up the good work and thanks for teaching us these scientific notations

  20. thank you for posting this Tyler its so understandable and educational keep up the good work and thanks for teaching us these scientific notations

  21. You have saved me, I'm in online school and the online textbooks they have are no help are very confusing, and emailing my teacher would take to long to respond. These videos have freaking saved my life and my grade.

  22. You're such a good teacher to us… (idk if you're really a teacher but if you are, you did a great job sir)ooppss correct me if I'm wrong ahhaha😂 just guessing🤔
    Thank you soooooo much! You help me a lot sir. 😘😊

Leave a Reply

Your email address will not be published. Required fields are marked *