Introduction to powers of 10

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 it's 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 tens and multiply them together so 10 times 10 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 one thousand and 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 so for example let's say I were to let's say I were to do this with ten tens so if I owe you 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 ten tens let's see one two three four five six seven eight nine ten 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 zeros one two three four five six seven eight nine ten we put the commas there so it's a little bit easier to read this right over here is ten billion and it's already getting kind of hard to write and 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 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 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 two would be called the exponent and the ten 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 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 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 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 100 100 times 10 is a thousand a thousand times 10 is 10,000 10,000 times 10 is equal to 100,000 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