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## Numbers & Operations - The Real & Complex Number Systems 211-217

# Introduction to powers of 10

Exponents are a way of simplifying the notation for repeated multiplication. When using a base of 10, the exponent tells you how many times to multiply 10 by itself. Converting between exponential notation and standard notation is straightforward: for example, 10 to the second power is the same as 10 times 10, or 100.

## Want to join the conversation?

- For the confused people, I'll give an example. Let's say you have 10 to the 4th power. you would add 4 zeros after the 1, giving you 10,000. The same thing goes for when you use different powers.

Ex: 10 to the 2nd power, 10 to the 3rd power, 10 to the 5th power, etc. etc

Even when you use numbers other than 10, this still applies.(39 votes)- You are right about ten, but 2^2=20 isn't correct.(19 votes)

- From0:36and beyond it made no sense to me but okay(15 votes)
- What is ten to the millionth power? It has to be a looooooooot!(7 votes)
- It would be 1 followed by 1,000,000 zeroes. Yeah. That's a lot. I think it's called a Googol, and it's written as 10^1000000.(4 votes)

- So if I were to do 10 to the power of 15 I would add 15 zeros, right?(5 votes)
- That is correct. But you have to make sure you are adding the zeroes to the first digit, one, or else your number may be 10 times too high.(7 votes)

- Let me make this easy for yall... First, you look at the little number above the big number. for example, ten to the power of six. you add six zeros to get the answer. or you can do it the hard way. your choice! but my teacher taught us the eeeeaaaassssyyyy way!

-thanks for reading, DUCKBABY.

P.S. not da baby... DUCKBABY(7 votes) - Is there a 10 to the -1 power?(6 votes)
- 10 to -1 power is equal to 1/10 when you have a negative exponent you always make it a fraction. For example 5 to the -1 power is equal to 1/5.

Hopes this helps:) And sorry for being 1 year late.(2 votes)

- Is he trying to do the power of ten you need to times 10×10×10=1,000 not 100 that answer is wrong because 10×10=100? The hat is BOB BBC.(5 votes)
- Ex:

10x10=100 100=10 to the second pattern. It's the same thing for each power of 10.Hope this helps anyone struggling. Tell me ay feedback if I explained wrong. Thanks in advance.(5 votes) - Does the base have to be 10 or can it be diferent?(4 votes)
- What does he mean we’re he says can you put another number here at4:02(3 votes)
- It means instead of the number being 10 to the power of 2, it can be 5 to the power of 2 or 3 to the power of 2. You can put any number you want and the same rules apply.(1 vote)

## Video transcript

- [Instructor] 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. So I could have just a 10. I could take two 10s and
multiply them together, so 10 times 10, which
you know is equal to 100. I could take three 10s and
multiply them together. 10 times 10 times 10 is equal to 1000. And I could do this
with any number of 10s. But at some point, if I'm
doing this with enough 10s, it gets pretty hard to write. So for example, let's say I
were to do this with 10 10s. So if I were to go 10 times 10 times 10 times 10,
that's four, that's five, that's six, that's seven, that's eight, that's nine, that is 10 10s. Let's see, one, two, three, four, five, six, seven, eight, nine, 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 one
followed by 10 zeroes. One, two, three, four, five, six, seven, eight, nine, 10. We put the commas there so it's just a little bit easier to read. This right over here is 10 billion, and it's already getting
kinda hard to write, and imagine if we have 30 10s 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. So the way they do this is through something known as exponents. Exponents. And so 10 times 10, we can rewrite as being equal to, if I have two 10s 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 10s and multiply them together and we're going to get 100. Just so you're familiar with
some of the parts of this, the two 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 1000? 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 10s and we see we're taking three 10s and we're multiplying them together. So this would be 10 to the third power. 10 is the base, three 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 1000. So this is really another
way of writing 1000. 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 were taking 10 10s and
multiplying them together. This is 10 to the 10th power. And 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 fifth 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 10s and multiply them together. So 10 times 10 times 10 times 10 times 10. And so 10 times 10 is 100, 100 times 10 is 1000, 1000 times 10 is 10000, 10000 times 10 is equal to 100000. So there you have it. You have the basics of exponents when we're dealing with 10, and I know what you were thinking. Can I put another number
here instead of 10? And the simple answer is, you can, but we're not gonna cover
that just yet in this video.