Below are the approximations of 1/13, 2/13, 3/13 series fractions
1/13 ≈ 0.07 = ( 0.076923)
2/13 ≈ 0.14 = ( 0.153846)
3/13 ≈ 0.21 = (0.230769)
4/13 ≈ 0.28 = (0.307692)
5/13 ≈ 0.35 = (0.384615)
6/13 ≈ 0.42 = (0.461538)
7/13 ≈ 0.49 = (0.538461)
8/13 ≈ 0.56 = (0.615384)
9/13 ≈ 0.63 = ( 0.692307)
10/13 ≈ 0.70 = ( 0.769230)
11/13 ≈ 0.77 = (0.846153)
12/13 ≈ 0.84 = (0.923076 )
I know these two fractions by heart.
1/13 = 0.076923 (This sequence only occurs with a numerator of 1,3,4,9 and 10.)
2/13 = 0.153846
You only have to calculate one decimal place and the rest results from the period.
I would like to know some Calculation techniques if you know, sir.
Do you use major system to remember expansions of the fraction ?
I always remember the numbers I want to calculate with as a direct image.
So there is no delay for me when remembering and calculating.
I would still advise developing solid numeracy skills and less reliance on memorization. If you learn to divide with two or three-digit numbers without problems, you will always be faster than with the memorized values. I used to do it for fun too. For example, I still know all fractions like 1/3, 1/7, 1/13, … 1/97 by heart but never use them for arithmetic.
@ynnad already showed the general rule.
To help memorize them more easily, it can help to understand some of the underlying mathematics. But that eventually amounts to two facts:
That’s correct, of course, but if someone is memorizing the sequences, they probably want to avoid doing the basic calculations. The fastest way is then usually the direct calculation. 
Thank you so much
Agreed. One one end of the spectrum, there is understanding with minimal memorization. As long as you know to start with 77 (2 digits) and follow what I wrote above, you can figure the rest out.
In the middle, is memorizing the sequences 076923 and 153864 (12 digits) and applying those to get the correct expansion for e.g. 7/13 = 0.538641…
The other extreme with minimal calculation and the greatest memory load is to memorize the 12 sets of repeating digits directly (72 digits total).
Different methods for different people / different goals.
Yep exactly. I memorized these values too. But unfortunately that time I wasn’t aware of major system like methods.
So I memorized that without any numbers system.
I was first interested in this when I see the value of 1/7…
After that I got interested in memorizing more values and not just 7.
I guess everyone know here about kevlah saptakam gunyat already. When I memorized , I memorized in the way mentioned below.
1/7 =>
I Love You : 143 × 999 (so much love of number 7)
142857 (If anyone know vedic maths rule : nikhilam navtascharamam dasatah, he have no problem here)
Then next values 2/7, 3/7, 4/7, 5/7, 6/7…
are have the pattern. If you check you can easily able to spot it.
143 = I love you
There is a movie in this name in our language
“143 I love you”
I am proud of your methods
