(0.0036)(2.8) / (0.04)(0.1)(0.003) =

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

\(=\frac{(36*10^{-4})*(28*10^{-1})}{(4*10^{-2})(1*10^{-1})*(3*10^{-3})}=\)

\(=\frac{36*28*10^{(-4-1)}}{4*3*10^{(-2-1-3)}}=\)

\(=\frac{3*28*10^{(-5)}}{10^{(-6)}}=\)

\(=84*10=840\).

Answer: A.
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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

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

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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

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
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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.

Useful concept: \(\frac{A \times B \times C}{D \times E \times F} = \frac{A}{D} \times \frac{B}{E} \times \frac{C}{F}\)

Rearrange the given expression as follows: \(\frac{(0.0036)(2.8)(1)}{(0.003)(0.04)(0.1)}\)

Rewrite to get: \(\frac{0.0036}{0.003} \times \frac{2.8}{0.04} \times \frac{1}{0.1}\)

PRO TIP: If you're having difficulty some of the individual fractions, recognize that we can create equivalent fractions by multiplying numerator and denominator by a power of 10.

For example, we can take \(\frac{0.0036}{0.003}\) and multiply numerator and denominator by \(10,000\) to get: \(\frac{36}{30}\), which simplifies to \(\frac{12}{10}\), which equals \(1.2\)

Similarly, we can take \(\frac{2.8}{0.04}\) and multiply numerator and denominator by \(100\) to get: \(\frac{280}{4}\), which equals \(70\)

And we can take \(\frac{1}{0.1}\) and multiply numerator and denominator by \(10\) to get: \(\frac{10}{1}\), which equals \(10\)


So our expression becomes: \(1.2 \times 70 \times 10\), which equals \(840\)

Answer: A

any similar questions to practise?

Check this: https://gmatclub.com/forum/topic144735.html

Check more in here: PS Arithmetic questions

Hope it helps.
_________________

30 second approach:

Work to get rid of the decimals for easy multiplication. Since the numerator contains one less decimal place compared to the denominator, tack on a 10 to the numerator.

(36 x 28 x 10) / (4 x 1 x 3)

As all cancel out evenly, there is no need to multiply.

36/3 = 12

28/4 = 7

12x 7 x 10 = 840