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# Multiplying & dividing in scientific notation

CCSS.Math:

## Video transcript

we have 7 times 10 to the 5th over 2 times 10 to the negative 2 times 2 point 5 times 10 to the 9th so let's try to simplify this a little bit and I'll start off by trying to simplify this denominator here so the numerator is just 7 times 10 to the 5th and the denominator I just have a bunch of numbers that are being multiplied times each other so I can do it in any order so let me swap the order so I'm going to do it to it's over 2 times 2.5 2.5 times 10 to the negative 2 times 10 to the negative 2 times 10 to the 9th times 10 to the ninth and this is going to be equal to so the numerator I haven't changed yet 7 times 10 to the fifth over over and here in the denominator 2 times let me do this in a new color now 2 times 2 point 5 is 5 and then 10 to the negative 2 times 10 to the 9th when you multiply two numbers that are being raised to exponents and they have the exact same base so it's 10 to the negative 2 times 10 to the negative 9 we can add the exponents so this is going to be 10 to the 9 minus 2 or 10 to the 7th so times 10 to the 7th and now we can view this as being equal to this is being equal to 7 over 5 7 over 5 times 10 to the fifth over 10 to the 7th times 10 to the 5th 10 to the fifth over 10 to the seventh 10 to the seventh we do then that orange color to keep track of the colors 10 to the seventh now what is 7 divided by 5 7 divided by 5 is equal to C it's one and two fifths or one point four so I'll just write it as one point four and then 10 to the fifth divided by 10 to the seventh so that's going to be the same thing as and there's two ways to view this you could view this as 10 to the fifth times 10 to the negative 7 you add the exponents you get 10 to the negative 2 or you say hey look I have I'm dividing this by this we have the same base we can subtract exponent so it's going to be 10 to the 5 minus which is 10 to the negative 2 so this part right over here is going to simplify 2 times 10 to the negative 2 now are we done have we written what we have here in scientific notation it looks like we have this value right over here is greater than or equal to 1 but it is less than it is less than or it's less than or equal to 9 it's a digit between 1 and 9 including one at 9 and we have and it's being multiplied by 10 to some power so this is it looks like we're done this simplified to one point four times 10 to the negative 2