What is the 57th digit to the right of the decimal point in the decima

Question

What is the 57th digit to the right of the decimal point in the decimal equivalent of 13/55?

A. 2
B. 3
C. 4
D. 5
E. 6

Rabab36 · Answer

dividing we get .2030603060...
recurring digits now except 2 digit rest follows pattern

55 digit left pattern of 3060 is repeated 
55/4 gives you 3

therefore 57 digit will be 6

stne · Answer

13/55 =.23636363...

We can see that the pattern repeats, Even positions are occupied by 3 and odd positions ( apart from first ) are occupied by 6.

57th position is odd and will be 6.

Ans E

Hope it's clear.

ScottTargetTestPrep · Answer

13/55 = 0.236363….

We see that all even digits are 3 and all odd digits, except for the first one are 6.

Thus, the 57th digit (an odd number) is 6.

Answer: E

shwetakoshija · Answer

To quickly convert between fractions and decimals, it is suggested that we memorise some key conversions: (From these, many many others can be derived.)

1/2 = 0.5
1/3 = 0.3333...
1/4 = 0.25
1/5 = 0.2
1/9 = 0.1111....
1/10 = 0.1
1/11 = 0.090909...

Now, let’s derive some more from these:

3/2 = 3(1/2) = 3(0.5) = 1.5
5/2 = 5(1/2) = 5(0.5) = 2.5
2/3 = 2(1/3) = 2(0.333...) = 0.6666...
1/6 = (1/2)*(1/3) = 0.5(0.333...) = 0.1666...
And so on.

Now this question wants 13/55. 
This is not a direct multiple of any of our memorised fractions. 
We can either take 13/55 as 13(1/5)(1/11) = 13(0.2)(0.0909...) OR do a small manipulation to make our numbers smaller.

13/55 = (11+2)/55 
This is equal to (11/55) + (2/55).
= (1/5) + (2/55)
= 0.2 + (2/55)

Now, 2(0.2)(0.0909...) is easier to calculate than 13(0.2)(0.0909...).

We have 0.4(0.0909...) = 0.0363636...

Finally, 0.2 + 0.03636... gives us 0.2363636....

Conclusion : Since all odd places except just the first one have 6 as a digit, the 57th digit will also be a 6.

sahiti220620 · Answer

Bunuel  can you please show that conversion to 1/99 fraction here and solve

egmat · Answer

sahiti220620  See if the below explanation helps:

Understanding the 1/99 Pattern

First, recall that  \frac{1}{99} = 0.\overline{01}  (01 repeats)

More generally:  \frac{N}{99} = 0.\overline{N}  where N is a 2-digit number that repeats.

For example:  \frac{36}{99} = 0.\overline{36} = 0.363636...

Converting 13/55 Using This Technique

Step 1: Find the decimal representation
 \frac{13}{55} = 0.2\overline{36}

Step 2: Separate the non-repeating and repeating parts
 0.2\overline{36} = 0.2 + 0.0\overline{36}

Step 3: Express the repeating part using 1/99
 0.0\overline{36} = \frac{0.\overline{36}}{10} = \frac{36/99}{10} = \frac{36}{990} = \frac{4}{110}

Step 4: Verify
 \frac{13}{55} = \frac{2}{10} + \frac{4}{110} = \frac{22}{110} + \frac{4}{110} = \frac{26}{110} = \frac{13}{55}  ✓

Finding the 57th Digit

Now we know:  \frac{13}{55} = 0.2\overline{36}

- Position 1:  2  (non-repeating)
- Positions 2 onwards:  36  repeats

For position 57:
- We need the  (57-1) = 56^{th}  digit of the repeating pattern " 36 "
-  56 \div 2 = 28  with remainder  0 
- This means we complete exactly 28 cycles of " 36 "
- The last digit of each cycle is  6

Answer: E (6)

Pattern Recognition Technique

When you see a fraction that produces a repeating decimal, immediately think:
- 1-digit repeat → denominator with factor 9
- 2-digit repeat → denominator with factor 99
- 3-digit repeat → denominator with factor 999

This  \frac{N}{99}  technique works whenever you can isolate the repeating part!

What is the 57th digit to the right of the decimal point in the decima

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What is the 57th digit to the right of the decimal point in the decima

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