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Scientific notation word problem: red blood cells

CCSS.Math:

Video transcript

a human body has 5 litres of blood 40% of which is red blood cells each red blood cell has a volume of approximately 90 times 10 to the negative 15 liters how many red blood cells are there in a human body write your answer in scientific notation and round to two decimal places so they tell us that they tell us the total volume of blood in the human body we have we have five liters so we have five liters and then they tell us that 40% of that 40% of that is red blood cells so if we take the five liters and we multiply by 40% this expression right here gives us the total volume of the red blood cells 40% of our total volume of blood now this is a total volume of red blood cells and we divide by the volume of each red blood cell then we're going to get the number of red blood cells so let's do that let's divide by the volume of each red blood cell so the volume of each red blood cell is 90 times 10 to the negative 15 liters liters so let's see if we can simplify so one thing that we can feel good about is that the unit's actually do cancel out we have new liters in the numerator leaders in the denominator so we're going to get just a pure number which is what we want we just want how many red blood cells are actually in the body so let's just focus let's just focus on the numbers here so five times 40 percent well five forty percent is the same thing as 0.4 so let me write that down this is the same thing as 0.45 times 0.4 is two so our numerator simplifies to 2 and in the denominator we have 90 times 10 to the negative 15 which isn't quite in scientific notation or actually it definitely is not in scientific notation it looks like it but remember in order to be in scientific notation in order to be in scientific notation this number has to be greater than or equal to 1 and less than 10 it's clearly not less than 10 we can convert this to scientific notation very easily 90 is the same thing as nine times ten or you can even say nine times ten to the first and then you multiply that times 10 to the negative 15 and then this simplifies to this simplifies to 9 times 10 to the well let's add these two exponents 10 to the negative 14 10 to the negative 14 10 to the negative 14 and now we can actually divide and let's simplify this division a little bit this is going to be the same thing this is going to be the same thing as 2 times as 2 over 9 is 2 over 9 x times 1 over 10 to the negative 14 well what's 1 over 10 to the negative 14 well that's just 10 to the 14 so this right over here is just the same thing as 10 to the 14 now you might say okay we just have to figure out what 2/9 is and we're done we've written this in scientific notation but you might already realize look two ninths is not greater than or equal to one how can we make this greater than or equal to one well we could we could multiply it by 10 if we multiply this by 10 then we've got to divide this by 10 to not change the value of this expression but let's do that so this is equal to if we multiply so I'm going to multiply this by 10 and I'm going to divide this by 10 so I didn't haven't changed I've multiplied and divided by 10 so this is equal to 20 over 9 20 over 9 times 10 to the 14th divided by 10 is 10 to the 13th power so what's 20 over 9 this is going to give us a number that is greater than or equal to 1 and less than 10 so let's figure it out and they wanted us to round I think they said round our answer to two decimal places so let's do that so 20 divided by 9 9 doesn't go into 2 it does go into 20 2 times 2 times 9 is 18 subtract get a remainder of 2 I think you see where this show is going to go get a remainder of 2 9 goes into 20 2 times 2 times 9 is 18 we're just going to keep getting twos so we get another to bring down to zero nine goes into 20 two times so it's really this thing right over here is really 2.2 repeating but they said round to two decimal places so this is going to be equal to two point two two times ten to the 13th power