\(\frac{(0.0036)(2.8)}{(0.04)(0.1)(0.003)}=\)

(A) 840.0
(B) 84.0
(C) 8.4
(D) 0.84
(E) 0.084

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

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.

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.

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

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

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
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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 ?

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

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