what is the 23rd digit in the expansion of 9/17?

Question

What is the 23rd digit in the expansion of 9/17 in this repeating decimal. fully detailed answer step by step

Answer 1

 

9/17= ?

using your calculator...

divide 9 by 17 and take all the digits except the last one

9/17=0.529411764 on my calculator

use only 0.52941176 and multiply it by 17

17*0.52941176=8.99999992

subtract 9 from this to get -0.00000008 and change the sign to +

divide 17 into 8

8/17=0.470588235

look at 0.52941176 and 0.47058823

put 47058823 at the end of 0.52941176 to get...

0.5294117647058823 so far ( I know that there are 16 digits in the repetend but you might not know, so keep working)

multiply 0.47058823 by 17 to get 7.99999991 and subtract 8 to get -0.00000009 and change the sign to +

when you divide 17 into 9 the digits will start to repeat because it's like starting all over again from the beginning (actually the remainders start to repeat so the digits in the repetend will start to repeat)

9/17=0.52941176470588235294117647058823...

the 23rd digit will be the 7th digit in the repetend, which is a 7 (16+7=23 !!)