How to divide 1 by numbers ending with 9

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How to Divide 1 by
numbers ending
with 9

Method 1

For example,
1/19 = ?

In the divisor (19),
previous one or
the number before
9 is 1.

By sutra, Eka
adhika or by adding
1 more to the
previous one, we
get 2.

So, “x” = 2

In this method,
we start from the
end

There will be
(divisor-1) terms
in the answer.

Step 1
Assign last number
to be 1 and multiply
it with “x”(i.e.2)
So. 21

Now go on
multiplying with
"x" for (divisor-1)/2
times (here,(19-1)/2
= 9 times)

if the multiplication is
more than 9 then put
unit and carry tens to
next digit

So, we get
9 4 7 3 6 8 4 2 1
Process:
(4x2)(7x2)(3x2)(6x2)(8x2)(4x2)(2x2)(2x1)(1)
814612168421

Step 2
In this step we will
subtract 999999999 –
(Figure got in first step)

So,
9 9 9 9 9 9 9 9 9
-9 4 7 3 6 8 4 2 1------------------------------
0 5 2 6 3 1 5 7 8

Now,
Write “0.”and then
answer of step 2 and
answer of step 1

So, 1/19=
0.052631578947368421

That’s it!

Following the same
steps,1/29,1/39,1/49,
can also be found in
seconds, if you
practice it.

For example,
1/29 = 0.0 3 4 4 8 2 7 5
8 6 2 0 6 8 9 6 5 5 1 7 2
4 1 3 7 9 3 1
(29-1=28 terms)

Method 2

Using method 1,
we can find 1/7,
1/13 etc. also

1/7 = (7/7)*(1/7)
= 7*(1/49)
where 1/49 can be
found out by method 1.

Also,
1/13=(3/3)*(1/13)
=3 * (1/39)
where 1/39 can be
found out by above
method.

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