If the digits 37 in the decimal 0.00037 repeat indefinitely,

Question

If the digits 37 in the decimal 0.00037 repeat indefinitely, what is the value of (10^5-10^3)(0.00037)?

A. 0
B. 0.37 repeating
C. 3.7
D. 10
E. 37

Traumer · Accepted Answer

Hi guys, for me the following approach made this question easier to handle:

(10^5-10^3)*0.000 37  =

(10^5*0.000 37 ) - (10^3*0.000 37 ) =

37. 37  - 0. 37  =

37

Bunuel · Answer

Assuming that answer E (37) is correct, then the question should be:

(10^5-10^3)*0.000(37)=?

(10^5-10^3)*0.000(37)=10^3(10^2-1)*0.00037=99000*0.000(37) .

0.000(37)=\frac{37}{99000}  (see Number Theory chapter of Math Book to know how to convert a recurring decimal to fraction).

So  99000*0.00(37)=99000*\frac{37}{99000}=37 .

Answer: E.

jakolik · Answer

Hi,

I am not sure about the first part of the equation. Is the question (105-103)*0.00037?

In general, below is the way to solve such questions that have decimals that repeat indefinitely:

1000x = 0.3737
100000x = 37.3737

1000x = 0.3737
100000x - 1000x = 37.3737 - 0.3737 
99000x = 37
x = 37/99000

Hope this is of use to you to solve the main question.

regards,
Jack

azule45 · Answer

are the answer choices correct here? i got 74/99000. how is the answer E? any explanations?

aimingformba · Answer

Thanks Bunuel. Sorry for the mess up with the powers...

snuffles563 · Answer

Hi Bunuel, arent you supposed to do the parenthesis first? so (10^5-10^3) becomes 10^2=100*0.0003737 .. where am I going wrong here? :oops:

suslik · Answer

Another way to solve is by opening parenthesis and multiplying 0.00037 by 10^5 and then by 10^3. If you notice the fact that 0.00037*10^3 will get rid of repeating 37s, the problem boils down to just multiplying 0.00037 by 10^5

Temurkhon · Answer

Instead of 99000*0.000(37), I just did 100000*0.000(37) and got 37.(37), so the closest is E

PareshGmat · Answer

This is wrong.  \frac{10^5}{10^3} = 10^2

As far as  10^5 - 10^3  is concerned,  10^5  is way high compared to  10^3

So,  10^5 - 10^3 \approx10^5

sashiim20 · Answer

Note : Rule to convert mixed recurring decimal to fraction : In the numerator write the entire given number formed by the (recurring and non - recurring parts) and subtract from it the part of the decimal that is not recurring. In the denominator, write as many nines as the number of digits recurring and then place next to it as many zeros as there are digits without recurring in the given decimal.

Converting the mixed recurring decimal ( 0.00037 )  37  repeat indefinitely] to fraction we get;

\frac{37-000}{99000} = \frac{37}{99000}

(10^5-10^3)(0.00037)

10^3(10^2-1)(\frac{37}{99000})

10^3(100-1)(\frac{37}{99000})

\frac{1000 * 99 * 37}{99000} = 37

Answer (E)...

anubhavece · Answer

We can just round it to 0.0004 and check the answer choices!

KarishmaB · Answer

Note that the answer options are very far apart so some approximation should have no impact.

10^5 is much greater than 10^3 so we can approximate (10^5-10^3) to be just 10^5

10^5 * .000373737 = approx 37.3737...

Answer (E)

SchruteDwight · Answer

My approach is as follows: (10^5-10^3)(\frac{37}{99}*10^{-3}) \implies 10^3(10^2-1)(\frac{37}{99}*10^{-3}) \implies 10^3(10-1)(10+1)(\frac{37}{99}*10^{-3}) \implies 10^3*37*10^{-3} \implies 10^0*37=37 Kudos are very much appreciated

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the digits 37 in the decimal 0.00037 repeat indefinitely,

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the digits 37 in the decimal 0.00037 repeat indefinitely,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards