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. Jordan Ambrose says:

Thank you you make it easier and I have a test tomorrow! Thank God for you.

2. Als says:

thanks Tyler, you rock. This helped a great deal.

3. Masse Thiam says:

i swear u the best

4. Nikolai Tenoso says:

Thanks 😀 you've been a biiiiiig help in my exams ..

THANKS!!!!

6. Natalja Milani says:

Thank you so much! VERY HELPFUL!!!

7. Alasdair Nation says:

Very helpful. But for the love of god, if you ever have a child, name it Booker

8. Wafa Sherin says:

Why would anyone dislike this video 😭😭

9. Skyy Cash cow says:

I like thanks!!

10. Lulune Monexe says:

omg thx this is very very helpful

11. Bobby stanhope says:

Thank you for making these awesome videos!

12. RAZ A. SHAMIA says:

13. Its Sheshebaa says:

one word i can say;

understandable

14. Bruna R says:

Thank you so much!!!!!! You actually make chemistry look easy. Do not stop teaching. You sure have a gift.

15. Alozie Chibueze says:

I checked for understanding scentific notation, but didn't find it.

16. Diamondgaming says:

Thanks

17. elizarrezs says:

18. Rick De La Garza says:

What about a number like 21,003?Where zeros are in between the numbers.

19. DW Music says:

You're awesome dude I wish you could teach Chemistry at my school

20. AriesMale88 says:

Hey look another time jump. Nice

21. Rama Alsouss says:

thanks a lot you're awesome

you make it very easy

22. Scrubble Dubble says:

thank you you helped me a lot

23. Mrs. Lisa says:

You explain everything so effortless. Thank you!

24. Vids for truth 765 says:

Wish you were my teacher and not the one I have. SHE STINKS!

25. Professor Finesser says:

Life save. Would of failed my test if it weren't because of you

26. Jessagrl89 says:

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! 🙂

27. Alan Bikoev says:

THANK YOU!!!!!!!!

28. Myase Saleh says:

If he teaches every subject, he would become a teacher monopoly!

29. Kobe Miller says:

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.

30. Bukuru Emmanuel says:

I'm starting to get it a little bit thank you so much!!!

31. Kitty Marie Rose says:

why can't you be my chemistry teacher ? 🙁

32. Abby The Unicorn says:

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

33. ERIC KaSSIS says:

Thank youu
Really helped:)

34. Kellie Krueger says:

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!

35. Dieter Carrasco says:

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)

36. Gulcan kiris says:

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

37. Zyga F says:

(9:40) -1.002000 has 7 significant digits but -1.002*10^6 has only 4 significant digits. Is it no problem?

38. Spring Castrodes says:

i learned this at the start of 6th grade

39. Heidi Gulley says:

THANK YOU!!!!!!!!!!!!!!!!👍👍👍👍👍👍👍👍👍👍🤓

40. PublicSpeaking202 says:

Fabulous teaching! Where is the recommended video "Understanding Scientific Notation"?

41. Tyronjames Cases says:

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

42. Tyronjames Cases says:

cant find any videos of it

43. Kathie L says:

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.

44. Northern Warfare says:

Dude your awesome whenever my old teacher cant help me I am coming here right away

45. Mala Rodriguez says:

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.

46. Imani Jones says:

i was so confused thanks for the help you should do one for the power of tens for 7th grade (:

47. Toni Atsaves says:

Thank you so much. Teachers take too much for granted, as if we should already know things.

48. Peace begins with a smile. says:

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

49. Daniel Banuelos says:

thank u u saved my project

50. Maya مايا says:

omg you are the best of the best thank you keep on going you are great I understand a lot plz wish me luck I have a test!😊

51. Alina Hamilton says:

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!!

52. Nono Bee says:

What's the answer of 4786 x 10 raise to (-8) power

you best than my profesor

54. NoName says:

This guy might have accually helped me not get a super bad grade on my test

55. Keyaira Goff says:

hiiiiiiiii

56. Rasha Alrifae says:

thank you so much tyler <3 <3

57. cherry blossoms says:

You're so good at teaching👏👏

58. Gill Corpus says:

Tyler Thank you so much! u are by far the greatest person who has explained this.

59. Andrea Herrera says:

You are the best at explaining scientific notation I was able to understand my cookbook better.

60. Hela Bear says:

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

61. sicilianotoronto says:

62. Mathew Leon Guerrero says:

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!!!

63. Rida Nisar says:

it's now clear for me.. thank God

64. rupesh jindal says:

cool!!

65. Xiomara Colon says:

cool

66. Hufflepuff says:

I wish you were my professor

67. Aon Doe says:

These videos have been excellent for review and self-study. Thank you Tyler.

I get it finally!! Studying for me cset

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!!

70. aman manandhar says:

oww its awesome bro

71. Jasmine Mellien says:

Thank the God above! Very well explained, thank you.

72. Stephanie 7674 says:

Thank you! You are soooo helpful! 😘

73. Jvillvin says:

I dont get it

74. stavros houiris says:

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

75. Leah Hicks says:

These videos make studying so much easier! Thank you for helping me with my chemistry!

76. Amrita Biswas says:

Nc

That helped

78. Edlin Faith de Asis says:

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!!

79. Lola Liang says:

The guy is so cute, I come here even though I don't need to learn chemistry… just for fun

80. ThePikamaster says:

thank you so much
ive been struggling in math lately a lot and his helps!

81. Susrita Mishra says:

Sir please make some videos on organic chemistry

82. di1996 di1996 says:

Vrry good video

83. Edwin Seu Amigo says:

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

84. Daniela On Fire! says:

I got confused with the two to 9:12

85. C Charm says:

con academy is a con doesn't like cometition

86. Zsofia Quartz says:

What is the scientific notation of 832 kg?

87. Virtus. Throw says:

What if its only 3? Or any kind of number but only given a single digit?

88. carlo llido says:

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

89. carlo llido says:

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

Keep math.

91. Kelebale Mosutlhane says:

help me write 973.50 in scientific notation

92. Angelina Ochoa says:

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.

93. B1ack 0p35 says:

100/10

94. Xyrell Andrainne Demecillo says:

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. 😘😊

95. RAVI SHARMA OFFICIAL says:

96. RAVI SHARMA OFFICIAL says:

97. Cristian Gomez says:

Thank you! This video helped me understand Scientific Notation more!

98. ASWATH GOWRISHANKAR says:

Thanks for the video it was really easy for me to understand

99. Mathematics and science class 9 to 12. says:

Hi
U r videos are so useful and make interesting in chemistry.
Thank u

100. Krishna Gurjar says:

Thanks sir