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

Introduction to powers of 10


3m read
·Nov 11, 2024

In this video, I'm going to introduce you to a new type of mathematical notation that will seem fancy at first, but hopefully, you'll appreciate is pretty useful and also pretty straightforward. So let's just start with some things that we already know.

I could have just a ten. I could take two tens and multiply them together. So, ten times ten, which you know is equal to a hundred. I could take three tens and multiply them together. Ten times ten times ten is equal to 1000. I could do this with any number of tens, but at some point, if I'm doing this with enough tens, it gets pretty hard to write.

For example, let's say I were to do this with ten tens. So, if I were to do ten times ten times ten times ten, that's four, that's five, that's six, that's seven, that's eight, that's nine, that is ten tens. Let's see: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. This is going to be equal to, even the number that it's equal to is going to be quite hard to write. It's going to be 1 followed by 10 zeros: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Let me put the commas there so it's a little bit easier to read. This right over here is 10 billion, and it's already getting kind of hard to write. Imagine if we had 30 tens that we were multiplying together.

So, mathematicians have come up with a notation and some ideas to be able to write things like this a little bit more elegantly. The way they do this is through something known as exponents. Exponents. So, 10 times 10, we can rewrite as being equal to. If I have two tens and I'm multiplying them together, I could write this as 10 to the second power. That's how someone would say it; they would say 10 to the second power. That looks fancy, but all that means is let's take two tens and multiply them together, and we're going to get 100.

Just so you're familiar with some of the parts of this, the 2 would be called the exponent and the 10 would be the base. So, 10 to the second power is 10 times 10 is equal to 100.

So how would you write 10 times 10 times 10 or a thousand? How would you write that using exponents? Pause this video and see if you can figure that out.

Well, as exactly as you might have imagined, we're taking a certain number of tens, and we see we're taking three tens and we're multiplying them together. So, this would be 10 to the third power. 10 is the base; 3 is the exponent. We would read this as 10 to the third power. If you ever saw 10 to the third power, that means, "Hey, let me multiply 10 times 10 times 10." That's the same thing as a thousand. So this is really another way of writing a thousand.

And what about this number here, 10 billion? What's a way that we could write it using exponents? Pause the video and figure that out.

Well, as you might have imagined, we're taking 10 tens and multiplying them together. This is 10 to the 10th power. We can go the other way around. If someone were to walk up to you on the street and say, "What is 10 to the 5th power?" What is that? What number that you're probably familiar with would this be?

Well, this would mean that we're going to take five tens and multiply them together. So, 10 times 10 times 10 times 10 times 10. And so, 10 times 10 is 100. A hundred times ten is a thousand. A thousand times ten is ten thousand. Ten thousand times ten is equal to one hundred thousand.

So there you have it. You have the basics of exponents when we're dealing with 10. And I know you were thinking, "Can I put another number here instead of 10?" And the simple answer is you can, but we're not going to cover that just yet in this video.

More Articles

View All
Earth's changing climate | Earth and society | Middle school Earth and space science | Khan Academy
Have you ever tried to imagine what the world was like in the distant past? Maybe you’d like to explore the age of the dinosaurs, when the Earth was much hotter than it was today. Perhaps you’d prefer when temperatures dropped to much colder than today. Y…
Real Estate Tricks: How To Pay Off Your Home Mortgage FAST
What’s up you guys? It’s Graham here. So here’s a really popular topic of discussion when it comes to real estate, and that is how to pay off your mortgage early. With this video, I will tell you exactly how to do this with ninja real estate secrets and t…
Specific heat capacity | Khan Academy
Pop Quiz! We have two pots of water at the same temperature, say room temperature of about 30° C, as we want to increase this temperature to, say, 40° C. The question is, which of the two will take more heat energy? What do you think? Well, from our dail…
Writing geometric series in sigma notation
So we have a sum here of 2 plus 6 plus 18 plus 54, and we could obviously just evaluate it, add up these numbers. But what I want to do is I want to use it as practice for rewriting a series like this using sigma notation. So let’s just think about what’…
How can an atheist call Hitler evil?
Andrew made a video, uh, in which he asks the question to atheists, was Hitler evil? Um, I think the gist of his question is the idea—uh, the idea behind it is that, uh, because atheists don’t have a universal sense of right and wrong, can they condemn Hi…
NERD WARS: Thor vs. Kratos -- Who Would Win?
Hey everybody! It’s the wacky Gamers. Okay, Adam’s lame but it’s us! It’s Jeff and Adam. I’m Adam and we’re here to do another versus video. Yes, we are! A lot of people seem to like them, so we’re going to keep going. But this time, it’s another user sug…