Vulgar Fractions to Decimals Shortcut

How to convert vulgar fractions to decimals using Vedic Maths Shortcut?

Explanation

Expressing the vulgar fractions into decimal values is simple with the use of the Vedic maths shortcut.
Vulgar fractions denominator ends with 9

To solve the vulgar fraction into a decimal numbers follow the steps given below.
For example, let us consider the number 1/19.
Denominator ends with 9 example

To know the number of decimal values, take the denominator value and subtract it with one.
19 - 1 = 18 (hence we have 18 decimal place values for this fraction and after 18th decimal value the answer will be repeated).

Step 1: Take the first digit of the denominator and add one.
In 19, take the first value, 1+1 = 2.
Denominator ends with 9 step1

Step 2: Add one with the denominator.
19 + 1 = 20. So its 1/20
Denominator ends with 9 step2

Step 3: Divide 1/20.
1/20 = 0 (quotient) , 1(remainder)
Denominator ends with 9 step3

Step 4: Now write down the remainder followed by the quotient. It is 10.
Denominator ends with 9 step4

Step 5:
Divide Step 4 result by Step 1 result.
10/2 = 5(quotient), 0(remainder)
Denominator ends with 9 step 5

Step 6: Write down the remainder followed by the quotient from Step 5 and divide by Step 2 result.
05/2 = 2(quotient), 1(remainder)
Denominator ends with 9 step6

Step 7: Write down the remainder followed by the quotient from Step 6 and divide by Step 1 result.
12/2 = 6(quotient), 0(remainder)
Denominator ends with 9 step7

Step 8: Repeat the process till you get 18 decimal values.

Step 9: Write down all the quotient values from the result of the above steps.
1/19 = 0.0526...
Denominator ends with 9 step9

Let us use this shortcut for another example, 1/29.
29 - 1 = 28. So the fraction has 28 decimal values.
Step 1: Take first digit of denominator and add it with one.
2 + 1 = 3.
Step 2: Add one with the denominator, 29 + 1 = 30. So its 1/30
Step 3: Divide 1/30
1/30 = 0 (quotient) , 1(remainder)
Step 4: Write down the remainder followed by the quotient. It is 10.
Step 5: Divide the Step 4 result by Step 1 result.
10/3 = 3 (quotient), 1(remainder)
13/3 = 4(quotient), 1(remainder)
14/3 = 4(quotient), 2(remainder)
24/3 = 8(quotient), 0(remainder)
Repeat the same procedure till you get 28 decimal values.
Now the decimal fraction of 1/29 is 0.03448..