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Manager  B
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 51
GMAT Date: 10-01-2012
What is the 18th digit to the right of the decimal point  [#permalink]

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15 00:00

Difficulty:   55% (hard)

Question Stats: 62% (01:36) correct 38% (01:56) wrong based on 558 sessions

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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

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Joined: 01 Sep 2010
Posts: 3404
Re: What is the 18th digit to the right of the decimal point  [#permalink]

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2
$$\frac{1}{37}$$ 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)

D is the answer
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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]

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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

Regards,
Manish Khare
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Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
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Re: What is the 18th digit to the right of the decimal point  [#permalink]

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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)

D is the answer

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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GMAT 1: 660 Q47 V34 GPA: 4
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Re: What is the 18th digit to the right of the decimal point  [#permalink]

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Time taken 27 secs

Multiply the numerator and the denominator by 27.

so, 1/37= 27/27*37 = 27/999 = 0.027027... (Property of terminating decimal)

Hence, 7

-----------------------------------
Hit kudos if you appreciate the method or suggest a different approach  Re: What is the 18th digit to the right of the decimal point   [#permalink] 19 Oct 2018, 13:24
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What is the 18th digit to the right of the decimal point

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