We now take examples of 1 / a9, like 1/19

We now take examples of 1 / a9,

where a = 1, 2, -----, 9. In the

conversion of such vulgar fractions

into recurring decimals, Ekadhikena Purvena process can be effectively used both in division and

multiplication. 

Multiplication Method: 

Value of 1 / 19 

First we recognize the last digit of the denominator of the type 1 / a9. 

Here the last digit is 9. For a fraction of the form in whose denominator 9 is the last digit, we take the case of 1 / 19 as follows:

For 1 / 19, 'previous' of 19 is 1. And one more than of it is 1 + 1 = 2. 

Therefore 2 is the multiplier for

the conversion. We write the last digit in the numerator as 1 and follow the steps leftwards. 

Step. 1 : 1

Step. 2 : 21(multiply 1 by 2, put to

left)

Step. 3 : 421(multiply 2 by 2, put to

left)

Step. 4 : 8421(multiply 4 by 2, put to left)

Step. 5 : ¹68421 (multiply 8 by 2=16, 1 carried over, 6 put to left) 

Step. 6 : ¹368421 ( 6 X 2 =12+1 = 13, 1 carried over, 3 put to left ) 

Step. 7 : 7368421 ( 3 X 2, = 6 +1 = 7,

put to left)

Step. 8 : ¹47368421 (as in the same process)

Step. 9 : 947368421 ( Do – continue

to step 18)

Step. 10 : 18947368421 

Step. 11 : 178947368421 

Step. 12 : 1578947368421 

Step. 13 : 11578947368421 

Step. 14 : 31578947368421

Step. 15 : 631578947368421

Step. 16 : 12631578947368421 

Step. 17 : 52631578947368421

Step. 18 : 1052631578947368421 

Now from step 18 onwards the same

numbers and order towards left

continue. 

Thus 1 / 19 = 0.052631578947368421 

Find the recurring decimal form of

the fractions 1/29, 1/39, 1/49, 1/59, 1/69, 1/79, 1/89 using Ekadhika process.