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# Simplifying in scientific notation challenge

CCSS.Math:

## Video transcript

let's see if we can simplify this expression right over here and write it in scientific notation so the first thing I want to do well I already have parts of this expression that are written in scientific notation for my brain to simplify the multiplication I like to write everything into scientific notation and then do whatever I need to do to get it into a final product into scientific notation so this part right over here is 0.2 is not in scientific notation in order for it to be scientific notation it would we have to be some number between 1 and 10 not including 10 so greater than or equal to 1 less than less than 10 being multiplied by some power of 10 and this is clearly less than 1 but we could just view this as look this is this is in the tenths place this is 2 times 1/10 1/10 is 10 to the negative 1 so this is the same thing as 2 2 times 10 to the negative 1 same thing as 2 times 1/10 now if we look in the denominator in blue we have this part it is written in scientific notation but this green part is not but we could easily write it as this is 5/10 thousands ten thousand is five is ten to the fourth so this is the same thing as five times ten to the fourth power you see that it has one two three four zeros so now let's take the product in the numerator in the denominator so the numerator I'm just going to swap the order in which I'm multiplying I'm just multiplying a bunch of stuff 4.6 times 10 to the sixth times 2 times 10 to the negative 1 it doesn't matter what order I multiply them in so I could rewrite this as 4.6 times 2 times 2 times 10 to the sixth switching colors times 10 to the sixth times 10 to the negative 1 times 10 to the negative 1 and then in the denominator I've got five times well let me just write the five times two point three times two point three times 10 to the fourth times 10 to the fourth times 10 to the negative 2 times 10 to the negative 2 and now let us attempt to simplify this thing so here we have 4 point 6 times two let me circle that so 4.6 times two is nine point two so that's nine point two and then 10 to the sixth times 10 to the negative one we have the same base we're taking the product we can add the exponents is going to be 10 to the 6 minus 1 or 10 to the fifth power so times 10 to the fifth power so we've simplified our numerator and now in our denominator in our denominator let's see five times two point three five times two is 10 5 times 0.3 is 1.5 so it's going to be 11 point five so this is going to be 11 point five and then if I multiply 10 to the fourth times 10 to the negative 2 that's going to be 10 to the 4 minus 2 or 10 squared times 10 to the second power and now I can divide these two things so this is going to be equal to I'll have to think about what nine point two over eleven point five is but actually let me just do that right now get a little practice dividing decimals so nine point two give some real estate here so nine point two we do that same color nine point two divided by eleven point five divided by eleven point five well if we multiply both of these times ten that's the exact same thing that's the exact same thing as 92 divided by 115 we're essentially moved the decimal to the right for both of them and let me add some zeros here because I suspect that I'm going to get a decimal here so let's think what this is going to be let's think about this 115 doesn't go into nine it doesn't go to 92 it does go into 920 and I'm going to eyeball and say that it will go eight times let's see if that works out so my decimal here that's zero eight times eight times five is forty eight times 11 is 88 and then 88 plus 4 is 92 I went in exactly very good its 920 we have no remainder so 9.2 divided by eleven point five simplified to 0.8 0.8 and then 10 to the fifth divided by 10 to the second that's going to be the same thing as we have the same base and we're dividing so we can subtract the exponents that's going to be 10 to the 5 minus 2 or 10 so this right over here is going to be 10 to the third power so times 10 to the third power now are we done well in order to be done this number right over here needs to be greater than or equal to 1 and less than 10 it is clearly not greater than or equal to 1 so how can we rewrite this as the product of something that is greater than or equal to 1 and less than 10 and some power of 10 well this 8 right over here this is in the tenths place it's 8 tenths 8 times 1/10 we could rewrite it as so this is going to be the same thing as 8 times 10 to the negative 1 power and then we have this 10 to the third here so times so times 10 to the third power we do that in that other color times 10 to the third power and now we have the same base just add the exponents so this is going to be equal to 8 times 10 to the 3 minus 1 so 8 times 10 squared and we're done we've simplified our original expression