** Fractional number convert in to decimal in one line**

Vulgar fractional number **whose denominator ending by 9** like, 1/19, 1/29, 4/39 etc. will be convert in to decimal number in one line by using Ekadhikena purvena sutra of Vedic Mathematics.

There are two method in Vedic Mathematic to solve this fraction number.

1)Multiplication Method

2)Division Method

We will learn both the methods, you can apply any one which will be easy to understand.

**1)Multiplication Method:**

**Beauty of this method is that we get our answer without doing any division.**

In this method we get our answer from right to left, means we get our last digit first & then we move towards left side. The number of digits we will get after decimal point is depends upon the fractional number, but we can stop when series is getting repeated.

**Ex. i) 1/19**

For 1/19, denominator ending by 9, so we can apply our sutra Ekadhikena Purvena. Ekadhikena purvena means **one more than previous**. In denominator 19 previous number is 1 & one more than previous is 1 + 1 =2.

So, here **2 is the constant multiplier for whole conversion** of the fraction.

**Step 1:** As we start from right to left so first, we find right most digit.

**Numerator = 1 is our right most digit**.

1/19 = 0. **1**

** **

**Step 2: **As 2 is our multiplier, multiply rightmost digit 1 x 2 =2. Write down 2 to the left side of 1.

1/19 = 0. **2**1

**Step 3: **Now multiply this 2 by multiplier 2, 2 x 2 = 4, Write down 4 to the left side of 2.

1/19 = 0. **4**21

** **

**Step 4: **Multiply 4 X 2 = 8, write down 4 to the left-hand side of 4

** **1/19 = 0. **8**421

**Step 5: **Multiply 8 X 2 =16, so now we write down 6 to the left-hand side of 8 & carry over 1 in our next digit

1/19 = 0. _{1}**6**8421

**Step 6: **Multiply 6 X 2 = 12 + 1 (carry over) = 13, So we write down 3 & carryover 1

1/19 = 0. _{1}**3**68421

**Step 7: **Multiply 3 X 2 =6 + 1(Carryover) = 7, so we write down to the 7 left-hand side of 3

1/19 = 0. **7**368421

Do continue till step 18

1/19 = 0. _{1}**4**7368421 —(8)

1/19 = 0. **9**47368421 —(9)

1/19 = 0. _{1}**8**947368421 —(10)

1/19 = 0. _{1}**7**8947368421 —(11)

1/19 = 0. _{1}**5**78947368421 —(12)

1/19 = 0. _{1}**1**578947368421 —(13)

1/19 = 0. **3**1578947368421 —(14)

1/19 = 0. **6**31578947368421 —(15)

1/19 = 0. _{1}**2**631578947368421 —(16)

1/19 = 0. **5**2631578947368421 —(17)

1/19 = 0._{1}052631578947368421 —(18)

Now from step 18 onwards same series of the number start to repeat, so we stop here,

** **

**Note: The maximum number of decimal places before repetition start is,**

** Denominator – Numerator**

** 19 -1 = 18 places**

**Number series may repeat before (Denominator – numerator) obtained number also, so we must stop when number series gets repeated. **

** **

**Ex 2) 4 / 39**

** **

** **If we check denominator, it ends by 9 so we can apply our trick here.

In 39, previous digit is 3, one more than previous is 3+1 = 4

** So, here 4 is our constant multiplier. And numerator 4 is our last digit of decimal**

** **Now steps are already explained in above sum, so we directly write down answers,

4/39 = 0. **4** (Numerator as last digit)

4/39 = 0. _{1}**6**4 (4 X 4 =16)

4/39 = 0. _{2}**5**64 (6 X 4 =24 + 1=25)

4/39 = 0. _{2}**2**564 (5 X 4 =20 + 2=22)

4/39 = 0. _{1}**0**2564 (2 X 4 =8 + 2=10**)**

4/39 = 0. **1**02564 (0 X 4 =0 + 1=1**)**

4/39 = 0. **4**102564

We can observe that series is started to repeat from here, so we stop

** **

**Ex 3) 5/23 **

Denominator is not ending by 9, but we can convert it in that form, by multiplying 3 to both denominator as well as numerator.

Now, denominator ends by 9, so we can solve by Vedic method.

In 15/69, previous digit is 6, one more than previous is 6 + 1 =7 so, **our constant multiplier is 7 & numerator is 15, which is our last digit.**

** **

15/69 = 0. _{1}5( we write down 5 as a last digit & carry over 1)

15/69 = 0. _{3}65( 5×7 = 35 + 1(carry)=36)

Similar way we continue.

15/69 = 0.2173913043478260869565

After that series is started to repeat.

** **

**2) Division Method**

**In division method we get our solution from left to right.**

**We will solve same example that we solve by multiplication method. **

** **

**Ex i) 1/19**

**Here also in 19 previous digit is 1, so one more than previous is 1 + 1 =2**

**So, 2 is our constant divisor**

** **

**Step 1: **Numerator is 1 so we divide it by divisor 2.

1/2, (Q = 0 & R = 1)

1/19 = 0._{1}0 (Q = 0 is our first digit & R = 1 we write down to the left-hand side of 0)

As our divisor is fixed i.e. 2, & dividend is the number generated by Reminder & quotient.**(RQ)**

So here dividend is 10

** **

**Step 2: **Divide 10 by 2 (Q = 5, R =0)

1/19 = 0.0_{0}5 (As above step we write down Q = 5 as our second digit & R = 0 at left hand side of 5)

So, our new dividend is 05(RQ)

**Step 3: **Divide 5 by 2 (Q = 2, R =1)

1/19 = 0.05_{1}2

** **

**We will repeat the step till the number series is not repeated**

** **

**Step 4: **Divide 12 by 2 (Q = 6, R =0)

1/19 = 0.052_{0}6

** **

**Step 5: **Divide 6 by 2 (Q = 3, R =0)

1/19 = 0.0526_{0}3

** **

**Step 6: **Divide 3 by 2 (Q = 1, R =1)

1/19 = 0.05263_{1}1

** **

**Step 7: **Divide 11 by 2 (Q = 5, R =1)

1/19 = 0.052631_{1}5

** **

**Step 8: **Divide 15 by 2 (Q = 7, R =1)

1/19 = 0.0526315_{1}7

** **

**Step 9: **Divide 17 by 2 (Q = 8, R =1)

1/19 = 0.05263157_{1}8

**Similarly, we repeat the step up to step 18,**

**After step 18 our answer will be,**

1/19 = 0.05263157894736842_{0}1

Now after step 18, divide 1 by 2 so our step 1 will be repeated so we stop here,

**Find this links to study more:**

1. Criss-Cross method of multiplication

i love vedic math !!!!!!!

i love vedic math