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# What is the 18th digit to the right of the decimal point

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What is the 18th digit to the right of the decimal point [#permalink]
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Pansi wrote:
What is the 18th digit to the right of the decimal point in the decimal expansion of 1/37?

(A) 0
(B) 2
(C) 4
(D) 7
(E) 9

$$\frac{1}{37}=0.027027...$$

So, we have a repeating cycle of 027. Every third digit (3rd, 6th, 9th, ...) to the right of the decimal point is 7, thus 18th digit to the right of the decimal point is also 7.

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Re: What is the 18th digit to the right of the decimal point [#permalink]
Always remember GMAT never asks for complex calculations .So whenever you see questions like this ,try to identify the pattern .In this case ,the fraction is a recurring decimal 0.027027027... 027 keeps on repeating .18th digit is 3*6 so 7 is the answer

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Manish Khare
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Re: What is the 18th digit to the right of the decimal point [#permalink]
carcass wrote:
$$\frac{1}{37}$$ could be a difficult or at least if not approched well could lead to the wron answer or prone of error

So, do $$\frac{100}{37}$$ in this way is more comfortable and in the end you will add 2 zeros

we want the 18 th number and 18 is even

$$\frac{100}{37}$$ $$=$$ $$270270$$ ------------> $$0.0270270$$

Now notice the first number is 0 second 2 third 7 and the fourth again 0

So $$4 * 4 = 16$$ in our pattern.

So is $$ZERO$$ $$+ 2 = 7$$ ( be carefull we are talking of units place not sum)

hi
how can you say so ...?

.027 027 027

here we can see a set of "027" composed of 3 digits, NOT of 4 digits ...
to find the 18th digit, we can arrange 6 identical sets as shown above. Clearly the 18th digit is 7...

thanks ...
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Re: What is the 18th digit to the right of the decimal point [#permalink]
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Re: What is the 18th digit to the right of the decimal point [#permalink]
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