MCAT Math Vid 4 – Scientific Notation for Addition, Subtraction, Multiplication and Division


Leah here from Leah4sci.com/MCAT and in this
video, I’ll show you how to use Scientific Notation in MCAT style questions without a
calculator when it comes to addition, subtraction, multiplication and division.
When it comes to adding and subtracting exponents as long as you’re dealing with the same power
all you have to do is add and subtract the coefficient and keep the power. So for example,
say you’re given 4.7×10¯³ + 2.3×10¯³ . Both numbers in the question are times 10 to the
minus 3 so all we have to do is add 4.7 and 2.3. Let’s We’ll start with the coefficient,
4 and 2 is 6, point 7 and point 3 is 1 gives us a total of 7.0×10¯³. Ten to the minus
3 hasn’t changed and all I did was add the two numbers.
When the powers are not the same but they’re close enough, you want to turn them into the
same power and then treat it the same way. Let’s keep it simple, say I have 5×10¯³
+ 6×10¯⁴ . I can’t simply add 5 and 6 because I’m dealing with different powers. So what
I wanna do is turn the first number into the power of negative 4 or the second number into
a power of negative 3. In an earlier video I showed you a trick for multiplying and dividing
by a factor of 10 by simply moving the decimal. You can find that video along with my entire
MCAT Math without a Calculator series on my website leah4sci.com/MCATMATH. Scientific
Notation is simply another way to represent powers of 10 and if I treat it that way, the
trick of moving decimals still applies. If I have the number like 10¯³ the way to make
this to 10¯⁴ is to divide it by 10. Now remember the trick I showed you, if I have
an example and I do times 10 divided by 10, I don’t change the identity of the example.
So if I take 10¯³ and divide that by 10, I get 10¯⁴. I have to justify that by multiplying
this number (5) by 10. 5×10 is 50. Changing 5×10¯³ to be 50×10¯⁴ has the same exact
value. Now that I have 50×10¯⁴ I can add that to 6×10¯⁴ because they have the same
power. 50 + 6 is 56 and we still keep 10¯⁴. Now in typical Scientific Notation, you want
just one number immediately followed by a decimal. So I have to do that times ten divided
by ten again or simply think of it as when I decrease the number, meaning I move the
tens place decimal 1 space to the left, I increase my exponent value. So 56 divided
by 10 is 5.6, 10¯⁴ times 10 is 10¯³. In other words, I use that trick again of
times 10 divided by 10 and quickly got my answer. So the final answer for this question
is 5.6×10¯³. Multiplication of Exponents may show up on
your MCAT in question like this: Find the NO3- concentration when 6.8×10¯⁷
moles NANO₃ are added to 5.1×10¯³ L of H20.
Finding molarities on topic that will be discussed in the Chemistry series at leah4sci.com/MCATChemistry,
but for now let’s focus on Math. We want to solve for Molarity which is mol/L (M=mol/L).
On the numbers out of the the question, we have an equation like this :
M=mol/L=6.8×10¯⁷ / 5.1×10¯³ mol/L This throws off so many students because they
make it harder than it has to. So let’s talk about the rules then let’s solve the problem.
When it comes to Multiplication, all you do is multiply the number and then ADD the exponents.
(2×10⁴)(4×10²)=8×10⁶ -In this case we have 2×4 which is 8. For the exponents 10⁴
and 10² we add 4 and 2 which is 6 giving us an answer of 8×10⁶.
For Division, you divide your numbers and then Subtract your exponents. In this case
we have 3 x 10⁶ ÷ 6 x 10³ , we’ll set that up
as follows: 3 divided by 6 that’s 3/6, we can simplify that to 1/3 which is 0.33, this
is the fraction that you have to know. If you don’t know it yet, grab my MCAT Math guide
on my website http://leah4sci.com/MCATMath. Next we subtract the exponents, we have 10⁶
and 10³, 6 minus 3 is 3 giving me an answer of .5 x 10³. Now this is not proper Scientific
Notation so we’ll actually move the decimal 1 space to the right multiplying by 10 and
decrease the exponent by 1 number which is essentially dividing by 10, in other words
we’re multiplying and dividing by 10 giving me an actual answer of .5×10² or simply 500.
Now back to our question. For a question like this, the MCAT is not looking for the exact
value, instead they are looking for something close enough and you’ll typically see answers
that have the powers all over the place. So we’re looking for an approximate number but
the correct power. The power in this case is 10¯⁷ divided by 10¯³ so we have 7
minus negative 3. Negative 7 minus negative 3, Minus Negative cancels out so it’s really
Negative 7 plus 3 (-7+3) giving me a new exponent of 10¯⁴. The numbers themselves 6.8 is
approximately 7, 5.1 is approximately 5 so we have 7/5 x 10¯⁴. This is not an appropriate
answer and in the next video I’ll break down fractions and ratios in more detail but for
now look at it this way; 7/5 is really 5/5 + 2/5 5/5 is 1 so we have 1 and 2/5 x 10¯⁴.
Two over Five (2/5) is a fraction you should recognize because one over five (1/5) is point
two (.2), therefore Two over Five (2/5) is point four (.4). This gives us a final answer
of 1.4 x 10¯⁴. Punching the initial numbers into the calculator, I got 1.33 x 10¯⁴
which on the MCAT is close enough. Be sure to join me in the next video where
I show you how to tackle Squares and square roots when it comes to the MCAT.
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22 Comments

  1. cha yang said:

    Leah you are the BEST!…. I used your videos to overcome Ochem 1 and 2.. Now I'm using your videos again to study for the MCAT… Thanks so much!

    June 12, 2014
    Reply
  2. Valerie Martinez said:

    Thank you so much for your videos.  I was struggling with time in the PS because of long calculations. You are an awesome teacher. Best wishes.

    August 16, 2014
    Reply
  3. Medina Sareini said:

    If I could ever meet you, I want you to know that I would give you the BIGGEST WARMEST HUG EVER AND TAKE YOU OUT DINNER. In all seriousness, thank you for these amazing videos. Your ability to take seemingly complicated processes and transform them into something anyone can understand is beyond me. Thank you, thank you a million times,

    May 17, 2015
    Reply
  4. everberry51 said:

    these videos are great!!! thank you!!

    July 11, 2015
    Reply
  5. Michal Twardowski said:

    I wish I had found this earlier. I'm taking the MCAT tomorrow and feel okay, but the way you present all this material is brilliant. It really attenuates the terror that the MCAT's complexity tries to induce. Thank you so much I'll definitely be using these principles to weed out traps and clearly incorrect answers!:)

    August 21, 2015
    Reply
  6. zoya haroon said:

    Actually… I failed MCAT😢 and now I'll give my MCAT again in august 2016

    January 26, 2016
    Reply
  7. Addie A said:

    You may have just saved my score!!! thank you

    May 5, 2016
    Reply
  8. Rebi333 said:

    How do you do the trick when you have 3/5? since there is nothing that adds up to 3 that equals 5. In your example you did 7/5=5/5+2/5

    August 2, 2016
    Reply
  9. D D said:

    Your introduction is so satisfying to watch in the beginning of each video haha.

    November 4, 2016
    Reply
  10. alex ruuska said:

    Leah, you are helping me feel confident about my math abilities! I didn't realize how many of these rules I already seem to know and how I have already solved problems like these before in my pre-med classes. That tells me I am just psyching myself on PS practice, and that I don't have any reason to. You make it seem like this type of problem solving is actually much easier than what I've had to do for classes, because it is! Thank you so much!

    March 6, 2017
    Reply
  11. marena hanna said:

    Question: why wasn't 0.5 x 10^3 an appropriate answer?

    July 15, 2017
    Reply
  12. Piyush Kumar said:

    thanks you help me lot

    July 29, 2017
    Reply
  13. Keyur Patel said:

    I was going through your videos for review of basic mathematics principles, and ended up learning a new trick, never really thought about doing the whole 5/5 + 2/5 deal, always kinda just estimated – 7.5/5 = 1.5, so it's a little bit under 1.5 is what I'd do, but your trick's better

    July 31, 2017
    Reply
  14. Christian Anaya said:

    Quick and to the point, easily accessible you should teach at my University.

    September 2, 2017
    Reply
  15. James Daylon said:

    It’s very helpfull thanks
    You are the best teacher

    October 24, 2017
    Reply
  16. Allen Mol said:

    damn girl, youre killing it in these videos

    May 9, 2018
    Reply
  17. Victoria Wood said:

    i owe you my life

    May 22, 2018
    Reply
  18. princess goodridge said:

    How were you able to get 5/5 + 2/5. Did the denominator remain the same and you split the numerator? Also I was confused after this part. If you could assist in helping me with how you found 1.4.

    November 8, 2018
    Reply
  19. HeartLiz said:

    Bless you. I struggle with math so much and decided after I graduated with a music degree that I wanted to pursue a career in medicine.

    February 10, 2019
    Reply
  20. Ghulam Haider said:

    OMG thank you so much my math had gotten so rusty but you really are a life saver !!!! thank you so much

    May 28, 2019
    Reply
  21. jahmiaherbert88 said:

    Thank you Leah I've tried the Examkrackers but I was stuck on their practice problems. You made it more simple for me to understand. I appreciate you and your skills. Again Thank you!!!!!

    June 14, 2019
    Reply
  22. Tricia Leftwich said:

    You are my hero!

    July 21, 2019
    Reply

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