yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Scientific Notation - Explained!


3m read
·Nov 10, 2024

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 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?

More Articles

View All
Warren Buffett: How to Make Money During a Recession
So it seems like pretty much everyone is worried about the economy right now, and for good reason. Inflation is at a multi-generational high. The last time inflation was this high in the United States was in 1981, more than four decades ago. In order to g…
Stop Trying and You'll Succeed
There’s nothing worse than a sleepless night. We’ve all been there, tossing and turning. You focus all your mental power on trying to fall asleep. With all your will, you force yourself to shut your eyes, turn your brain off, and pray to be whisked away i…
Mr. Freeman, part 04
Hi, how many people are there! What are you chewing? Mmm… I thought trophy canned food. Common, enough! Draw your attention away from your meal and let’s imagine… You are a rich manufacturer. Yes-yes, you are. On the excellent tall ship, you carry brocad…
Distillation curves | Intermolecular forces and properties | AP Chemistry | Khan Academy
[Instructor] In this video, we’re gonna dig a little bit deeper into distillation, and in particular, we’re gonna learn how to construct and interpret distillation curves. So let’s say we’re trying to distill roughly 50 milliliters. That is 50% methyl a…
Good Things Are Coming Into The Crypto Landscape! | Kitco NEWS
[Music] Kevin: Great to have you with us. Roy: Thank you! Great to be here. Kevin: Alright, Kevin, as wonderful as it is to have Mr. Wonderful, we also have quant maestro and Bitcoin OG Roy Niederhoffer. Roy has been a Bitcoin bull since 2011. He’s the…
Watch Koko the Gorilla Use Sign Language in This 1981 Film | National Geographic
[Music] Near San Francisco, California, a fascinating and now controversial experiment has been underway since 1972. Research psychologist Penny Patterson is teaching lowland gorillas Koko the American Sign Language of the deaf. Dr. Patterson claims Koko …