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
Finding inverses of rational functions | Equations | Algebra 2 | Khan Academy
All right, let’s say that we have the function f of x and it’s equal to 2x plus 5 over 4 minus 3x. What we want to do is figure out what is the inverse of our function. Pause this video and try to figure that out before we work on that together. All righ…
Buffer capacity | Acids and bases | AP Chemistry | Khan Academy
Buffer capacity refers to the amount of acid or base a buffer can neutralize before the pH changes by a large amount. An increased buffer capacity means an increased amount of acid or base neutralized before the pH changes dramatically. Let’s compare two…
Would You Choose Life On Earth Or in Space? #kurzgesagt #shorts
Spending your entire life in space. If there’s another planet suitable for humans, it will be quite a long journey to get there. Even traveling at one percent of the speed of light, it would still take 10,000 years to go only 100 light years. This means …
From the Ashes - Official Film Trailer | National Geographic
[Music] Ralph Waldo Emerson wrote, “Coal is civilization and power.” From the early 1900s to World War II, coal powered America. We’re still quite dependent on coal, but coal was a nineteenth-century source of fuel, and we’re in the 21st century. The tow…
The Fermi Paradox: Where are all the Aliens?
Liftoff from a tropical rainforest to the Edge of Time itself. James Webb begins a voyage back to the birth of the Universe. On December 25th, 2021, NASA launched the successor to the Hubble Space Telescope, the James Webb Space Telescope. Hubble has pro…
Don’t forget the “viable” part.
If you can’t get anyone to use your MVP, it’s probably not an MVP. Well, it’s not the V; we’re missing the V, which is viable. Like, basically, if it doesn’t work for anyone, yeah, how hard to argue that it’s viable? No, and like, shouldn’t an MVP— it see…