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## Scientific notation word problems

# Scientific notation word problem: red blood cells

CCSS.Math:

## Video transcript

A human body has
5 liters 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 the total volume
of blood in the human body. We have 5 liters. And then they tell us that 40%
of that is red blood cells. So if we take the 5 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 the 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. So let's see if we can simplify. So one thing that we
can feel good about is that the units
actually do cancel out. We have liters in the numerator,
liters 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
the numbers here. So 5 times 40%-- well 40%
is the same thing as 0.4. So let me write that down. This is the same thing as 0.4. 5 times 0.4 is 2. So our numerator
simplifies to 2. And in the denominator, we have
90 times 10 to the negative 15, which definitely is not
in scientific notation. It looks like it, but
remember, 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. But we can convert this
to scientific notation very easily. 90 is the same
thing as 9 times 10, or you could even say 9
times 10 to the first. And then you multiply that
times 10 to the negative 15. And then this
simplifies to 9 times-- let's add these two exponents--
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 as 2/9 times 1 to t 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, OK, we just
have to figure out what 2/9 is and we're done. We've written this in
scientific notation. But you might have
already realized, look, 2/9 is not greater
than or equal to 1. How can we make this
greater than or equal to 1? Well 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 I'm going to
multiply this by 10, and I'm going to
divide this by 10. So I haven't changed. I've multiplied
and divided by 10. So this is equal to 20/9 times
10 to the 14th divided by 10 is 10 to the 13th power. So what's 20/9? 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 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 two times. 2 times 9 is 18. Subtract. Get a remainder of 2. I think you see where
this show is going to go. 9 goes into 20 two times. 2 times 9 is 18. We're just going to
keep getting 2's. So we get another
2, bring down a 0. Nine goes into 20 two times. So 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 2.22 times 10 to the 13th power.