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Ann K

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Decimal numbers

How can I solve these kind of problems in my brain without using pencil and calculator?

2.3*10^7*5.2*10^-5/4.3*10^2
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Ann K

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But in MCAT exam i am only allowed to use my brain.
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Also, aren't you allowed to scribble stuff on the margins to ease the burden on your brain?
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Oh yes they are multiple choices questions. It says in the MCAT preparation book that I am not allowed to use any kind of calculator or pencil.
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Approximations may be good enough to eliminate most of the choices.
5.2/4.3 ~ 52/44 = 13/11
2.3 ~ 22/10
And the 11 divides nicely into the 22 leaving 2.
So an approximate answer is 2*13/10 = 2.6
That binds the numbers implicitly differently than I bound the numbers.
>> 2.3 * 5.2 * 4.3
Should  be
2.3 * 5.2 / 4.3 = 2.781 instead of the 2.6 that I approximated.
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5.23 * 34.25
How to do this without using calculator or paper?
Is your expression correct, because it does not have brackets
You bound the numbers as per the OP. I started with a guess that maybe the author forgot to include the parenthesis in the denominator since that would make the powers of 10 all cancel out - something that I would expect in a MCAT exam which I used to tutor in years ago. I even helped one girl get into osteopathic college of medicine.
Oh lumpheaded me. I did not see the /4.3. I thought it was all multiplication and exponents.

So

10^7*10^-5*10^2 is 10,000

2.3 * 5.2 / 4.3 is about 2.5  so 25,000 close to the 27,000 Excel formula.
Ann,
If you want really good responses o on the fastest way t solve these math problems, you must post the questions as you see them; namely with the multiple choices.
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I copied it from the book.

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How to do this without using calculator or paper?   5.23 * 34.25

5*30 = 150     5*40 = 200    5*35 is halfway between 175.  The actual answer will be a little larger.
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Thanks guys. This exam is really tough.
Thank you and sorry about my initial error (* instead of /)
D-Glitch and I pointed out that the powers of 10 cancelled out. From the multiple choices you can see that they are partly testing you on that point.

Here are the rules you must be proficient in.

10^a * 10^b = 10^(a+b)

10^a / 10^b =  10^(a-b)



You can replace the number 10 with another positive number.
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Thanks phoffric. This one I understand. The only issue is with the decimal numbers. numerator / demonitor or multiplying both.

For instance: 23.456 * 1.23
Like this is hard for me or if they are dividing.