Scientific Notation – Explained!


In science, we often have to deal with some
very large numbers. For example, the mass of the sun. That is the mass of the sun. Two followed
by thirty zeros in units of kilograms. That is two thousand billion billion billion kilograms.
There has got to be a better way to write that. Can you imagine if there wasn’t? And
so we find that the mass of the sun is two zero zero zero zero zero zero zero zero zero.
Yes? Sorry could you repeat that? I was with you up to two zero zero zero zero zero? Ahh?
It was ahh… two zero zero. So to represent large numbers easily, we use something called
scientific notation. Scientific notation takes advantage of powers of ten. For example, ten
to the power of two means take two tens and multiply them together. And you get 100. Ten
to the power of three means multiply three tens together. And you get 1000. Ten to the
power of four means take four tens and multiply them together. And you get 10,000. So you
should notice a pattern developing. When it’s ten to the power of two, our final answer
has a one followed by two zeros. Ten to the power of three, our final answer has a one
followed by three zeros. Ten to the power of four, again, four zeros. So if we wanted
to represent the mass of the sun in scientific notation, we would need thirty zeros. So we
represent that using ten to the power of thirty. This means that we’re multiplying ten by itself
thirty times, which gives us a one followed by thirty zeros. But the mass of the sun is
actually twice that. It’s two followed by thirty zeros so we can multiply two by ten
to the thirty in units of kilograms and that is the mass of the sun. It’s much easier to
write and it takes up much less space on the page. The other problem is we have to deal
with some tiny numbers. For example the mass of a proton is… That is the mass of a proton. Zero point,
and there there are 26 zeros, and then 1673 kilograms. A truly tiny number so how do we
deal with this? Well again it’s using a similar trick. If we raise ten to the power of minus
one, it means divide by ten, not multiply by ten. So this means divide by ten which
gives you zero point one. Ten to the power of minus two means divide by ten twice, which
gives us zero point zero one, a hundredth. Ten to the power of minus three means divide
by ten three times, or zero point zero zero one. So again you see a pattern developing.
The exponent here tells you how many places to the right of the decimal that the one is.
So in this case, ten to the minus two, the one is two places to the right of the decimal.
Here, ten to the minus three, the one is three places to the right of the decimal. So in
this case I actually have a one that is 27 places to the right of the decimal. So I can
write the mass of a proton as 1.673 times ten to the minus 27 kilograms. And this ten
to the minus 27 has the function of putting this number, 1.673, 27 decimal places to the
right of the decimal point. So as a challenge question to see if you’ve understood it: if
the sun were made entirely of protons, how many protons would there be in the sun?

100 Comments

  1. Harsh Thakkar said:

    That's 7th grade math 😂

    January 13, 2017
    Reply
  2. Jay Nelson said:

    1.1954572624 x 10^57

    February 12, 2017
    Reply
  3. John Gabriel said:

    Thx for the help! 🙂 Every time we do Star Math, it always asks me stuff i don't even know like notations with 20 0s (it's frustrating and confusing, so I guess). My teacher told me my math grade level is 9th grade and I'm in 6th grade.

    February 16, 2017
    Reply
  4. Nicolino Will said:

    You could say the mass of the sun is 2 nonillion, however.

    March 2, 2017
    Reply
  5. Woo Wei Jie said:

    when dr derek is still young and hot af 😀

    March 9, 2017
    Reply
  6. The Terrarian said:

    1.195457262402869097429766885833831440526001195457262402869 * 10^57
    There, it is very efficient

    March 11, 2017
    Reply
  7. Talestory JL said:

    3:05 First time I've seen someone writing zeros that fast

    March 13, 2017
    Reply
  8. Wojak kajow said:

    This video really enlighted me about the scientific notation I 'learned' from school.
    I think that was for me what you said music meant to you for about 2 years, hehe :/

    March 14, 2017
    Reply
  9. Ezran Zulnaidy said:

    1.195*10^57….right

    March 20, 2017
    Reply
  10. Karly Sims said:

    Love it! Home schooling a 9th grader and a mama needs some reminders. Thanks for making it fun!

    March 23, 2017
    Reply
  11. Ed West said:

    1.195e57

    March 26, 2017
    Reply
  12. ohaRega said:

    1.195 x 10^57 protons…
    when you consider that there are approximately 10^80 atoms in the *universe*, that's a noteworthy amount.

    March 26, 2017
    Reply
  13. Pranay Shukla said:

    1.195×10^57

    March 29, 2017
    Reply
  14. Taneja G said:

    and the answer to the challenge question is 1.196172 followed by 57 zeroes

    April 4, 2017
    Reply
  15. davit nazarashvili said:

    (2*10^30)/(1.673*10^-27)=2:1.673*10^57=1.1954572624*10^57

    April 14, 2017
    Reply
  16. EebstertheGreat said:

    Why did Derek give the mass of a proton to four significant figures but the mass of the Sun to only one?

    April 24, 2017
    Reply
  17. Louis McKenna said:

    So helpful! thanks

    April 25, 2017
    Reply
  18. alex bluestein said:

    think about if the sun was made of just protons. the positive charge of the sun would be insane! it would attract every god damn electron on earth!

    May 3, 2017
    Reply
  19. Victor Oliveira said:

    My first guess would be 9 but I'm gonna go with brown as my final answer.

    May 4, 2017
    Reply
  20. Mr.Grass said:

    why write it as 2 x 10 (power 30) why not 20 (power 30)?
    why fuq u guys wanna soak up cums from our balls? make it easy bitch

    May 7, 2017
    Reply
  21. Jake From Snake Farm said:

    1,195,457,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 protons in the sun, if the sun's mass was entirely protons.

    May 12, 2017
    Reply
  22. Ian Soede said:

    This is cool and all and very nice but my physics teacher says that we always have to use this notation even if it isnt a big number, that sucks.

    May 26, 2017
    Reply
  23. Jerome Dienemann said:

    so it's 11954.572624, or am I missing something?

    June 1, 2017
    Reply
  24. Hazard Wolf said:

    Thx bro helped a lot

    June 9, 2017
    Reply
  25. SUBHADIP BARDHAN said:

    11.957..×10^57

    June 11, 2017
    Reply
  26. Abhigyan Rastogi said:

    the powers dont capture the emotion though.
    like look at the previous one 2 followed by 30 zeros and then look at 2×10^30 .

    July 7, 2017
    Reply
  27. Rope's Gun's said:

    1.1954573*10^57

    July 9, 2017
    Reply
  28. aditya mahimkar said:

    Number of protons in sun = 1195 x 10^60

    July 19, 2017
    Reply
  29. Dhruv Shah said:

    I like you videos

    July 25, 2017
    Reply
  30. Cargolplex said:

    Scientific notation is too small to describe huge number like G1 and Graham's number (G64).

    August 12, 2017
    Reply
  31. KILL3RXXD said:

    This the answer the the problem 3.346×10powerof 30

    August 22, 2017
    Reply
  32. Nig Nog said:

    BRO thnaks for the video saved mi day

    August 23, 2017
    Reply
  33. Pete VanDemark said:

    1.195 x 10^57 protons

    August 27, 2017
    Reply
  34. Bruce McConkie said:

    Interesting videos. And the ones where he explains subjects are really well done. He makes this subject easy to understand and use. Chem. is going to be a lot easier tomorrow. Thanks!

    August 29, 2017
    Reply
  35. Liam Uchiyama Arcila said:

    wuss poppin jim🅱️o

    September 11, 2017
    Reply
  36. Noosey said:

    yo hes kinda h0t

    September 12, 2017
    Reply
  37. Jerry Gundecker said:

    Question, Mr. Tassium: My brother and I live 10 mi. apart, but often a text takes 2 weeks to arrive. where do they hide out? or do they just swirl around c-clockwise in the north. hemisphere?

    September 23, 2017
    Reply
  38. Jack Liebig said:

    He says that 10/10 is 0.1 but it is just one

    September 26, 2017
    Reply
  39. CrimsonRose QH's said:

    I finally understand.

    September 27, 2017
    Reply
  40. itachi _uchihakiller said:

    Thanks that help me very much

    October 5, 2017
    Reply
  41. Killer Gamer said:

    thnks bro

    October 7, 2017
    Reply
  42. Rukhsana Zaidi said:

    You're sooo hot blushes

    October 9, 2017
    Reply
  43. Marcos Montoya-Diaz said:

    Hola

    October 13, 2017
    Reply
  44. Tom Holland said:

    1.673 x10^57?

    October 17, 2017
    Reply
  45. NemoPlays said:

    THANKS BRO! Now im sure ill get a good grade on my test. Thanks!

    October 19, 2017
    Reply
  46. Kolelo Karam said:

    2:08 did he just write the 💯 emoji?

    October 21, 2017
    Reply
  47. Despiser Despised said:

    At some point in a person's life it will be 50 years since you learned this stuff in school. A fun refresher course is always great.

    These videos should put the Unionized Public Sector "Teachers" out of business. Before they enslave our progeny to pay for their sedition.

    October 24, 2017
    Reply
  48. itz lebby said:

    Hi

    October 29, 2017
    Reply
  49. Wurst said:

    Could you repeat that? I thought he was going to say the whole thing.

    November 28, 2017
    Reply
  50. Ahmad Refaat said:

    1.19×10^57
    protons

    December 2, 2017
    Reply
  51. Ruben muro said:

    forheads brighter than my future

    December 12, 2017
    Reply
  52. Harzfrommarz said:

    For those who say they already knew this, why watch this video at all?

    January 3, 2018
    Reply
  53. Blan Morrison said:

    There is no way in the solar system that the mass of the sun is precisely 2 x 10^30 kilograms.

    January 18, 2018
    Reply
  54. TAI WAN XI - said:

    Oh come on Derek I'm just 13, how am I going to count the challenge question without knowing how to calculate it??

    February 2, 2018
    Reply
  55. Alam Gul said:

    SCIENTIFIC NOTATION:the scientific way to write large and small numbers is to express them in some power of ten

    February 13, 2018
    Reply
  56. LOTS said:

    one and six hundred seventy three thousandths multiply by ten power of fifty seven

    February 17, 2018
    Reply
  57. Monkey Gaming said:

    Great vid this really helped me

    March 1, 2018
    Reply
  58. Shell B. Atoms said:

    I love this video, and have shown it to my students every year when I teach scientific notation. I teach 5th grade. It's not only highly informative, but fun to watch. 🙂 THANKS!

    March 6, 2018
    Reply
  59. Alok Dhar Dubey said:

    1.195 * 10^(57)

    March 9, 2018
    Reply
  60. Bruno Berti said:

    1,19545 x 10^57

    March 15, 2018
    Reply
  61. Magnusatlas Derivia said:

    This actually helped me understand this a lot better thanks.

    March 29, 2018
    Reply
  62. R. Wright said:

    This homeschooling Mom thanks you!

    April 10, 2018
    Reply
  63. Pamir Popalzai said:

    Wow very well explained 😮thank you👍

    April 11, 2018
    Reply
  64. mech nical said:

    Gadha

    April 29, 2018
    Reply
  65. KAJAL SARKAR said:

    nicr

    May 5, 2018
    Reply
  66. KAJAL SARKAR said:

    nice

    May 5, 2018
    Reply
  67. Satya Devi said:

    thanks sir

    May 7, 2018
    Reply
  68. Kalpana Singh said:

    thank you sir…..now i am not having any confusion……i wish that you may make video like this only…which would be helpful for the students like me

    May 15, 2018
    Reply
  69. RaZe Phoenix said:

    Helped a lot

    May 22, 2018
    Reply
  70. Andrew Watson said:

    The number of protons composing the sun would be 1.195457262403X10^57kg.

    May 24, 2018
    Reply
  71. NJ Online Academy said:

    good

    June 9, 2018
    Reply
  72. Pete Lorenzo said:

    intriguing. I understand this, but I've always had trouble wrapping my head around a number when I get one from a calculator. my brain handles it better if I can see the actual number, not short-hand.

    June 20, 2018
    Reply
  73. Tushar Anand said:

    It's a 1.25×10^57 protons

    June 23, 2018
    Reply
  74. CeresTV said:

    The easier way to explain the small number notation is to say it's exactly like the large number notation, only backwards.

    June 24, 2018
    Reply
  75. James Bridgman said:

    1.195×10^57

    July 1, 2018
    Reply
  76. immaculateboy said:

    You sir are adorable.

    July 11, 2018
    Reply
  77. Jordylene Sagusay said:

    Thank u

    August 9, 2018
    Reply
  78. Dziobaczek Gadułka said:

    ~1,195*10^57 is the answer.

    August 13, 2018
    Reply
  79. Michelle Wilcox said:

    It's that time of the school year again! I so enjoy using this video to teach scientific notation to my 5th graders! THANKS! 🙂

    September 27, 2018
    Reply
  80. Xnoob Speakable said:

    Why do you use scientific notation just say the mass of the sun is 2 nonillion kilograms

    October 3, 2018
    Reply
  81. mohd kabir said:

    thanks sir for explaining this

    October 7, 2018
    Reply
  82. pk rasel said:

    1.1976*10^57 protons

    October 7, 2018
    Reply
  83. Jacob Rabon said:

    veritasium ur a god

    October 17, 2018
    Reply
  84. M m said:

    Great lesson Derek !! I loved that ❤🖒

    November 6, 2018
    Reply
  85. Frettchen YT said:

    There would be: 1.195*10^57 protons in the sun

    November 11, 2018
    Reply
  86. Ali Hamza said:

    I can smell the chalk

    November 17, 2018
    Reply
  87. Manuel Jesus Arredondo Ruiz said:

    Will there ever be Spanish Closed Caption? I see people have already worked on a translation.

    December 14, 2018
    Reply
  88. Piyush S. said:

    It is maths (exponents and powers) it is used in science

    December 23, 2018
    Reply
  89. OrangeOrb--SapphireSphere said:

    The answer. P=Mass of a single Proton in units of Kilograms. P= 1.1673×10^-27 Kilogram or just 1 Divided by this small number is the # of Protons in a Kg of protons. In other words 1 over P or 1/P Equals the defintive # of actual Protons in a Kg. Multiply the inverse of P=(1/P) by the Mass of the Sun in Kg and the answer follows is if you could place the Sun on one side of a scale and this many 1.1954×10^57 Protons on the other then you would have a balance.

    January 20, 2019
    Reply
  90. Alvin Enathan said:

    This is basic maths. Its like studying primary 5 and 6 maths.

    March 4, 2019
    Reply
  91. harsh kanu said:

    1.195×10^27 protons…

    April 13, 2019
    Reply
  92. Braden Sardina said:

    skit funny

    May 14, 2019
    Reply
  93. Henrik Kragh said:

    It is quite interesting (Some would say saddening) to see how my attention span has been modified (Some would say damaged) by culture and media here in 2019. I remember a time when I was nailed to the screen watching a cdk007 production, which was essentially a powerpoint presentation in video form. I just decided to go back and take a look at these very early videos of Derek's/Veritasium. And they are SOOO slow. The editing is off. They take forever to get to the point. Dammit. I know the videos are not to blame. I am. I want my old self back, who was less in a hurry, and had time to just sit back, and let the content flow at a lazy rate. Drinking coffee. Not worrying so much about time…

    May 19, 2019
    Reply
  94. Pure Playz said:

    MY MATH TEACHER JUST TEACHED THIS TO US AND SHOWED THiS VID AND mE AT SCHOOL WAS LIKE
    ME: VERITASIUM!!!! I KNOW THAT GUY

    July 19, 2019
    Reply
  95. Natalie Post said:

    THANK YOU SO MUCH!!!!!! This helped me so much! yay!

    July 21, 2019
    Reply
  96. ساره Dr. said:

    شكرا جزيلا

    July 29, 2019
    Reply
  97. Elijah said:

    my pee pee hARD

    August 16, 2019
    Reply
  98. Nourhan Rouda said:

    Hi isabelle

    September 8, 2019
    Reply
  99. Isabelle Bazzi said:

    Hi nourhan

    September 8, 2019
    Reply
  100. Aaron Truong said:

    Yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeieeeeeeeeeeeeieeeeeeeeeeeeleeeeereeerfreerrrrsrrrrrrttttt

    September 26, 2019
    Reply

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