\(\frac{0.0036*2.8}{0.04*0.1*0.003}=\frac{(36*10^{-4})*(28*10^{-1})}{(4*10^{-2})(1*10^{-1})*(3*10^{-3})}=\frac{36*28*10^{(-4-1)}}{4*3*10^{(-2-1-3)}}=84*10=840\).

Answer: A.
_________________

While reading the problem, I re-wrote in the following way:
36/10000 * 28/10 * 100 / 4 * 10/1 * 1000/3
Simplifying further, Answer = A = 840

I calculated the power of 10.
It was 10^5 / 10^-6.
Hence the ans. will end with 10^1. Its only A.

With questions like this, take a look at the answers first. Notice the only distinction between the answers is the factor of ten; thus, an exact calculation is not necessary to solve the problem, just a quick approximation.

.0036*2.8 is ~.0036*3, which can be approximated to .01.

.04*.1 = .004

Thus we have (.01)/(.004*.003). We can cancel out the powers of ten to give us 1/(.4*.003), which is 1/(.0012).

.0012 in fraction form is 12/10,000. Thus, our answer is can be given as 10,000/12.

840 is the only answer that comes close. Answer:A

Using the approximation method you can easily solve this question in 1:30 - 2:00.

36(28)*10^-5 / 12 * 10^-6


84 /10^-1 = 840

I think there is mistake in the last part of the solution.
84 /10^-1 = 840 . This should be 8.4 not 840.
84/10^1 = 840.

Let me know if my understanding is correct.

1/10^-1 = 10.. (the way i used power without symbol might create problem)

check below url..

Reciprocal in http://gmatclub.com/forum/math-number-theory-88376.html

With these kinds of equations the best thing to do is move the decimal places to the right, remember, what you move in the numerator has to occur in the denominator.

1) ORIGINAL EQUATION: (0.0036)(2.8) / (0.04)(0.1)(0.003)

2) MOVE 2.8 TWO PLACES TO THE RIGHT AND MOVE 0.04 TWO PLACES TO THE RIGHT, EQUATION THEN BECOMES: (0.0036)(280) / (4)(0.1)(0.003)
YOU CAN NOW DIVIDE 280 BY 4 - CANCEL OUT THE FOUR AND THE 280 BECOMES 70

3) MOVE 0.0036 ONE PLACE TO THE RIGHT AND MOVE 0.1 IN THE DENOMINATOR ONE PLACE TO THE RIGHT, EQUATION THEN BECOMES: (0.036) (70) / (1) (0.003)

4) AGAIN MOVE 0.036 TWO PLACES TO THE RIGHT AND MOVE 0.003 TWO PLACES TO THE RIGHT, EQUATION THEN BECOMES: (36)(70) / (1)(3)

5) CANCEL OUT THE THREE AND THE 36 TO FURTHER SIMPLIFY, YOUR EQUATION THEN BECOMES 12*70 = 840 WHICH IS ANSWET CHOICE A

Given that (0.0036)(2.8) / (0.04)(0.1)(0.003)
= [(36/1000)(28/10)] / [(4/100)(1/10)(3/100)]
= [(36*28)/(10000)] / [(4*1*3)/(100*10*100)]
= [(36*28)/(4*1*3)] * [(100*10*100) / 10000]
= (3*28) * 10
= 840
Hence option A

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course

I found my approach to be the quickest available and I'd like to share it with you guys:

(0.0036 x 2.8)/(0.04x0.1x0.003)
-> expand numerator and denominator by 10^6 (since there are 5 decimal places in the numerator and 6 decimal places in the denominator)
this yields:
(360x28)/(4x1x3)
-> cancel
(120x7)/(1x1x1)= 120x7 = 840 -> A

0.0036 = 36/10,000

Not sure if this is the right way to approach the answer, since the answer choices have big separation, I decided to approximate.
(0.0036)(2.8) / (0.04)(0.1)(0.003) = (4∗10^−3)∗(3)/[(4∗10^−2)(1∗10^−1)∗(3∗10^−3)] = 1*10^3 = ~1000
Closest Ans to 1000 is C: 840
_________________

i put everything in fractions, and it helped much.
[(36*28)/10,000 * 10] * (100*10*1000)/(4*1*3)

now, simplify and get 7*12*10 = 840
A

I multiplied all numbers by 10,000 to get integers hence

36 * 28000 / 400 * 1000* 30 = 210/ 2500 which is 0.084. Then answer is multiplied by 10,000.

0.084 *10,000 = 840

Answer A

Do you guys think it is a the fastest and the most accurate way ?

No need to calculate for non-zero terms as it has to be 84..
check the decimal points..
Numerator has 5 and denominator has 6, so answer should be 6-5 =1 digit after decimal point
or 84*10=840
_________________

Can anyone explain o me how can you easly simplify (28*36)/(4*3*10^(-1))???

DarioBaltazar

The 12 (4 multiplied by 3 in the denominator) divides the 36 in the numerator to leave 3 multipled by 28, which equals 84. You can then see that the 10^-1 can be flipped to give you 84 multiplied by 10 which equals 840 (choice A). Hope this helps.

I would not do approximation when you can solve this problem in 30 seconds.
For every place you move the decimal in the denominator, you do the same in the numerator and vice versa.
So you end up with (360*28)/(4*3) = 840

After reading the problem, I thought converting all the numbers to fractions will be an easier way to solve the question.

\(\frac{36}{10000}\) *\(\frac{28}{10}\) * \(\frac{100 }{ 4}\) * \(\frac{10}{1}\) * \(\frac{1000}{3}\).


On further reducing the fractions and simplifying, we are left with 3*28*10, which is equal to 840.

Therefore, the OA is A.