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Scientific notation word problem: red blood cells

Vampires and math students want to know: How many red blood cells are in the a human body? We can find the answer using scientific notation. Created by Sal Khan.

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  • leaf grey style avatar for user MadameDuFreak
    Why wouldn't you just divide the 9 into 2 and have the quotient of 0.22 there instead of ''borrowing'' the 10?
    (19 votes)
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    • female robot grace style avatar for user C C
      You could do that, and have 0.222 * 10^14. But then, to get it into official scientific notation, you would need change it to 2.22 * 10^13. So Sal is just doing the conversion into scientific notation in the earlier step. In both cases you would end up with the same answer,
      (31 votes)
  • leaf green style avatar for user Tyler Treaster
    Why was 1/10^-14 the same as 10^14? Not quite sure.
    (9 votes)
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    • starky ultimate style avatar for user Patrick
      Well, you can think it as (1/10)^-14. Then, according to the rule (a/b)^c = ((a^c)/(b^c)), you can use the distributive property:

      ((1^-14)/(10^-14)
      When a fraction has either a numerator or denominator or both with a negative exponent, you need to switch the position. Meaning the numerator with a negative exponent would switch to the denominator for a positive exponent, and vice versa.
      ((1^-14)/(10^-14)) = ((10^14)/(1^14))
      And since we know that 1 with a positive exponent is still one, it becomes:
      (10^14)/1
      And since division by one means the quotient is the dividend, it becomes:
      10^14
      Hope this is helpful.
      (4 votes)
  • female robot amelia style avatar for user Mathdragon300
    At in the video, you start to mention that 90 isn't in scientific notation because it isn't less than ten, which I agree with, but under that understanding, wouldn't 10^-15 technically not be in sci.n. because it isn't less than ten?
    (2 votes)
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    • leaf red style avatar for user Noble Mushtak
      90 isn't in scientific notation because the coefficient isn't less than 10. Since 90 is just a number, 90 is the coefficient which isn't less than 10.

      With 10^-15, the coefficient is 1 which is less than 10.

      However, it should be noted that to be in scientific notation, the coefficient must also be greater than or equal to 1.

      I hope this clarifies what Sal meant!
      (11 votes)
  • duskpin tree style avatar for user Christie
    At , Sal wrote "5 (liters) x 40%". Can someone show me how to work this out? ( You don't have to include the liters)
    (5 votes)
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  • starky tree style avatar for user ColeF
    this is old
    also how did he get the ten to turn into a nine that is some weird math right there. Does he have anymore things involving this kind of math because i still need to understand more.
    (4 votes)
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  • blobby green style avatar for user jennifer hux
    I realize I am the only person having trouble understanding this, but why did we divide by volume of 1 red blood cell rather than multiplying? total volume of 1 red cell/ volume of 1 cell = # of blood cells??

    I understand the calculation itself just confused on the formula
    (4 votes)
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  • orange juice squid orange style avatar for user Starzi
    At in the video, couldn't Sal have done 2/9 first, then made it into scientific notation, rather then multiplying it by ten? I'm kind of confused, whether I'm doing it right or wrong. Does both ways always work?
    (3 votes)
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  • spunky sam blue style avatar for user liza.williams
    In this video you added, you said to add 10^1 to 10^-15. The first time yo wrote it, you said it would be 10^-14. But the last few times you wrote it, you said 10^14. I thought it is still to be 10^-14. Why did you do that?
    (3 votes)
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  • blobby green style avatar for user Sean Ocampo
    What I don't get is why you would only multiply the 2 by 10 and not the 9 too.
    (1 vote)
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  • piceratops ultimate style avatar for user Paschal Curlin
    At , why did Sal have to multiply by ten on one side, but divide by ten on the other?
    (3 votes)
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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.