## Scientific notation 1

We’d express this really small

number in scientific notation. Let’s just see how

small it is. It is one, two, three,

four, five, six, seven, eight, nine zeroes. And then a 3457. All of that is behind

the decimal point. Now this is a bit of review

about scientific notation. It means expressing a number

in a form– let me give an example, it could be 5 times

10 to the fifth power. This would be an example

of writing something in scientific notation. And when you write something

in scientific notation, the number that you’re multiplying

by a power of ten, that number right there has to be greater

than or equal to 1, and it should be less than 10. And of course, this right here

is going to be a power of 10. So for example, if I were to

write 5 times 9 to the fifth, not scientific notation. If I were to write 50 times

10 to the fifth, not quite scientific notation. Sometimes this kind of gets by

for scientific notation while you’re doing computation. But if you really wanted to

write this in scientific notation, you would write this

as 5 times 10, which is 50 times 10 to the fifth. And 10 times 10 to the fifth

is 10 to the sixth. So you’d write this as 5

times 10 to the sixth. So your goal is always for this

number right here to be greater than or equal

to 1, less than 10. Likewise, if I wrote 0.9 times

10 squared, once again, not in scientific notation. You would want to write 0.9 as

9 times 10 to the negative 1 times 10 squared. And then this becomes

9 times 10. Which makes sense, because

0.9 times 100 is 90. 9 times 10 is 100. We could say 9 times 10

to the first power. So that was a bit of review. Let’s do it for this

problem right here. I guess a quick way to think

about converting this to scientific notation, think about

how many leading zeroes there are including the first

non zero number right there. So there are 10 digits to the

right if you include this 3. You have nine zeroes and

then you have this 3. So a very quick way to do it,

and I’ll explain in a second why it works, is we could

rewrite this right here as 3.457 times 10 to the, we had

nine zeroes, and then I count the 3, 10. So times 10 to the negative

10 power. And the reason why this makes

sense is, when you multiply something to a negative

power, you shift the decimal over to the left. Let me write it this way. Start with 3.457. And when you multiply it times

10 to the negative 10, you’re going to shift the decimal

to the left 10 spaces. So if you shift the decimal

to the left 10 spaces, what do you get? So if you shift it once, twice,

three, four, five, six, seven, eight, nine, ten. And of course, you can’t just

leave open space here. There’s going to be zeroes

there when you shift it. So you’re going to have one,

two, three, four, five, six, seven, eight, nine zeroes. And you can put a zero out here

just to make sure that you understand that there is a

zero in front of that decimal. And you get exactly what

we got up there. Another way to think about it

is, if you wanted to start with this really small number

and you wanted to get to 3.457, you could multiply

it by 10 to the tenth. That would shift this decimal

10 spaces to the right. So you could do this. And these are all the multiple

ways of looking at the exact same thing. You could write that 3.457 is

equal to this character. Or I could even copy and

paste this character. Times 10 to the tenth power. If you multiply by a positive

exponent, every time you multiply by 10 it shifts the

decimal to the right. It makes the number bigger. So if you multiply this by 10

to the tenth, this guy is going to move one, two, three,

four, five, six, seven, eight, nine, ten. It would shift it right there. And you’d get 3.457. So that’s the whole idea. 3.457 is this number times

10 to the tenth. So if you wanted to solve for

this number, you would multiply both sides of this

equation by 10 to the negative 10. So times 10 to the negative 10,

or that’s the equivalent of dividing by 10

to the tenth. These cancel out. Negative tenth is 10 to

the zero or just 1. And you get this thing over

here being equal to 3.457 times 10 to the negative 10. I just wrote it in a different

order over here.

bright and simple, congratulations a lot.

can you please tell me how the hell you got so smart? how do you know all this shit?

he took algebra

But what do I do with the negative exponent?

Can you do a scientific notation vidio on stuff like ( 1.8•10/11 ) ( 6.7• 10/12).

Thanks so much!

You’re amazing thaaaaaaank you so much ❤️