Rats   10 years AGO

5.678678678
.678678678 can be written as 678/999 since its a recurring decimal.
=5(678/999)
=(999*5+678)/999
=5673/999 (divide by 3 num. & den.)
=1891/333.......Ans

Like? Yes (15) | No (4)  

Harsh Poddar   10 years AGO

x=5.678678678......
1000x=5678.678678.....
Subtracting
999x=5673
x=5673/999=1891/333
option 7

Like? Yes (4) | No   

jagdish sharma   10 years AGO

x=5.678678.....
1000x=5678.678678....
1000x-x=5678.678678....-5.678678....
999x=5673
x=1891/333

Like? Yes (2) | No   

Ann Mary Jolly   10 years AGO

Ans : 1891/333
Let x be the rational no., x = 5.6786786786......
Then 10x = 56.786786....
and 10,000x = 56786.786786....
Now Subtracting 10x from 10,000x,since the decimal parts of two no.s are the same they'll be cancelled.
And so, 9,990x = 56786 - 56 = 56730 =>9990x=56730
Therefore, x = 5673/999 = 1891/333.

Like? Yes (2) | No   

Bholanath    10 years AGO

let y=5.678678...
1000y=5678.678678...
subtract both the equations,
999y=5673
y=5673/999
y=1891/333

Like? Yes (2) | No   

Triloki Shaw   10 years AGO

5672/999=5.677
4673/999=4.67
1891/333=5.6786786789

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Parveen Soni   10 years AGO

let a=given no. .............(1)
then 1000*a=given no. *1000.............(2)
(2)-(1) gives
5673/999 i.e 1891/333 option (7)

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Manish Singh   10 years AGO

when we divide 1891/333
we get 5.678678678678..... :)
so as ans gives the question,so option no 7.

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FAISAL RIZWAN   10 years AGO

1891/333=5.678678678678
so option 7 is correct

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Chandra sekhar reddy   10 years AGO

let x=5.678678678........
now 1000x=5678.678678.......
1000x-x= 5673.0
999x=5673
x=5673/999= 1891/333

Answer is 1891/333
Option is 7

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Manish Kumar   10 years AGO

1891/333 = 5.678678678678
option 7 is correct.

Like? Yes (1) | No   

Dharmendra Singh   10 years AGO

Ans. 7) is closest.
There is no other options that match up to three-four decimal places so need not to match all digits after decimal.
1891/333=5.6786.... only this option carry four digits of given question.
Note: you can also discard some option because they are not matching even single characteristics value.

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Krishna Chaitanya Boyanapalli   10 years AGO

1000x=5678.678678
x=5.678678
on solving x=5673/999=1891/333

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LAKSHMI ROJA   10 years AGO

by option verifying 1891/333=5.678678678...... so answer 1891/333 i.e.,option 7

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venkata bavani g   10 years AGO

tht is the only no which is divided by 333 which gives such a no as the ans

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Ravishankar Karn   10 years AGO

(5678-5)/999=5673/999=1891/333

Like? Yes (1) | No   

kumar sundram   10 years AGO

5.678678678=(5678-5)/999=5673/999=1891/333

Like? Yes (1) | No   

ravi shankar rai   10 years AGO

=1891/333=5.678678678

Like? Yes (1) | No   

Mayuresh Srivastava   10 years AGO

1891/333=5.6786786786786786786786786786787.

Like? Yes (1) | No   

MUKESH KUMAR   10 years AGO

1891/333= 5.678678678678

Like? Yes (2) | No (1)  

VAGU RAGHAVA ANJANI DIVYAVANI   10 years AGO

1891/333=5.678678678678

Like? Yes (1) | No   

neha selokar   10 years AGO

divide the options to get the answer
1891/333 = 5.6786787...

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Satyendra Singh   10 years AGO

divide and check no other options i think.

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NIDHI   10 years AGO

1891/333= 5.678678678678

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Guru Pranav   10 years AGO

choosing the values from options,
option 7 with 1891/333 satisfies the value of 5.678678678678

Like? Yes (1) | No   

Priya   10 years AGO

While dividing round off the last value

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Nagarjun N   10 years AGO

333*5.678678678678 = 1891

Like? Yes (1) | No   

Grishma Shah   10 years AGO

Multiplying 5.678678678678*333 = 1891

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Anantharaman   10 years AGO

1891/333 = 5.678678678678...

Option 7

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AMIT SINHA   10 years AGO

1891/333=5.678678678679

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Vinay Sipani    10 years AGO

As the decimals are recurring => denominator is a multiple of 3 or 11

From the options below,denominator is either 333 or 999

If denominator is 999 => numerator = 999 * 5.678 = 5673
If denominator is 333 => numerator = 333 * 5.678 = 1891

=> Number is 5673/999 or 1891/333

Hence option 7 is required answer

Like? Yes (1) | No   

Aakash Kumar   10 years AGO

.678678....=678/999=226/333
5.678678678....=(5*333+226)/333=1891/333

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Soham Yadav   10 years AGO

1891/333= 5.678678678678679
it is very near to given value. So ans is 7

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Dilip B Gauswami   10 years AGO

all divide value can be different the
but 7 1891/333=5.678678678678678678......repeat them..

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prateek jain   10 years AGO

1891/333=5.678678678678...

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manoj kumar mayrya   10 years AGO

in this question only two option is possible 1&7.
and 7is right answer

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KARUPPASAMY C   10 years AGO

1891/333=5.678678678678
so option is (7)

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Dipak Shaw   10 years AGO

its a reccuring problem
x=5.678678....
x=5+.678678...
x=5+(678/999)
x=1891/333

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krishnapriya   10 years AGO

1891/333=5.678678678678...

Like? Yes (1) | No   

PRATHAM MEHROTRA   10 years AGO

1891/333=5.678678678678

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Bhargaviinduri   10 years AGO

by verifying options we get ans op-7

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Ashfaque Hussain   10 years AGO

1891/333=5.678678678678
option 7 is correct

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prakash kumar   10 years AGO

5.678678678678.....
=5+0.678678678678.....
=5+678/999
=5673/999
=1891/333

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Shashi Kumar Gupta   10 years AGO

1891/333=5.678678678678

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Dinesh thatti   10 years AGO

1891/333=5.678678678678

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Anjai Baghel   10 years AGO

i am explaining this question by taking other example
like
We have .555.... --------(1)

Multiply both side by 10, we get 10*.5555=5.55...-----(2)

Subtracting (1) from (2) we get

9*0.55...=5

so we right 0.55..=(5/9)ans

Directly from the rule , we also get the same result .555.... has its period 5, so the numerator is 5. And as there is only one digit in the period, the denominator will have one nine. Thus, the vuglur fraction=5/9

of if .454545=45/99

or if 5.454545= 5(45/99)(this technique is used in this question)

Like? Yes (1) | No   

Neha Sharma   10 years AGO

1) 5672/999=5.677677677677678
2) 4673/999=4.677677677677678
3) 5673/333=17.03603603603604
4) 6753/343=19.68804664723032
5) 7653/233=32.84549356223176
6) 1891/999=1.892892892892893
7) 1891/333=5.678678678678679
8) 1981/333=5.948948948948949
9) 8911/999=8.91991991991992
so answer is 1891/333=5.678678678678......

Like? Yes (3) | No (3)  

prabhat kumar   10 years AGO

simply going through all option when 1891 divided by 333 we will get 5.6786787 . so the exact value of 5.678678678678 is 1891/333.

Like? Yes (2) | No (2)  

ashish   10 years AGO

Hit and trial method ........ No reason !

Like? Yes (1) | No (1)