Scientific Notation - Explained!

Scientists have to work with some very large and some very small numbers. To represent these numbers more easily, they use scientific notation. Scientific notation relies on powers of 10. This video gives examples of how to represent a large and small number and explains powers of ten.

[rhpmike]

All of the comments pointing out that people learn this in 6-9th grade are missing the point. Almost EVERYTHING Derek makes videos on is taught at some point in the education system, but people either forget it or have a fundamental misunderstanding. He's not trying to teach graduate level information. He's trying to correct the foundation that so many people have built upon sand.

[veritasium]

I see you've been watching numberphile... All good points but the number of protons is not just over half of a googol - it's much much less. Just as 10^2 is not half of 10^4 (it's 1%)

[ShellBAtoms]

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!

[nikolinapetrova]

LOL for the comment "Can you repeat that?"

[adrianmuresan]

I recommend this video to all my students, coming from all over the world, good private schools, all my students who do not have the habit of using the scientific notation. Thank you, Veritasium!

[moosefarms]

(2.0 x 10^30) / (1.673 x 10^-27) =
(2.0 / 1.673) x (10^30 / 10^-27) =
1.195 x 10^(30- -27) =
1.195 x 10^57 protons
yay math!

[thomasucc]

The mass of the sun = America's nation debt - 1

[masqueraze]

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

[veritasium]

@BAR2Q12 Sure - it would be unconventional but you could do it. Scientists prefer one digit in front of the decimal place for some reason.

[brucemcconkie]

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!

[thehobbit]

Love your video and many high schoolers need this too. Great job explaining. So I teach at an alternative high school and many of my student's traditional teachers gave up on them years ago and just ignored them. They need as much support as possible. This will help .a lot.

[myqueerfamily]

Why couldn't you have been my teacher when I was learning this stuff in high school? lol

[christianara]

Im a 5th grader
and thats helps SOOO Much with math work in school THANKS =)

[zdspider]

This was a good video. THIS is what Youtube should be about. Well done.

[BradenBest]

I think the carrot notation is pretty much the standard exponent delimiter in plain text.

It could also be written as 2 * 10^30 or 2(10^30) in algebraic exponential notation, or 2e+30 in IEEE standard exponential notation.

[ShaivyaHDhall]

Mr. Muller, you truly have a thing for this...amazing explanation and GREAT humor😂. Keep it up!👏🏻👍🏻

[lHenry]

(2/1, 673)*(10^30/10^(-27)) And if you have 10/(1/10) you just multiply 10 by the reciprocal value of (1/10) Wich is 10. So you can just add 30 to 27 so you have: (2/1, 673)*10^57 Wich is roughly 1, 1955*10^57 [Protons]

[gotjunkin]

now i learned a ton of this great video and after a decade i answer your challenge question
i asked how many protons would be in 1 kg
or how many (1.673 x 10 to the power of -27) are in 1kg
based on this equation ( 1 / 1.673 x 10 to the power of -27) = 5.977286312 x 10 to the power of 26
that is how many protons would be in each 1 kg of the sun so multiply that number by the sun's number of kilograms which's (2 x 10 to the power of 30)
and that equals (1.195457262 x 10 to the power of 57) protons
holly crap i may have just gotten this right!

[nathananiel]

1.) What is the large number representing? Hint: it was the mass of something very large in our solar system

2.) what was the small number representing? Hint: it’s part of a molecule

Can you guys help me with those questions?

[rubenito]

0:45. I just died with that level of cuteness. Sorry Dr.