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When the proper fraction\(\dfrac{n}{37}\)  is written as a repeating decimal, the sum of the first 40 digits to the right of the decimal point is 236. What is N?

When 1/148 is written as a repeating decimal, what is the 2016 digit to the right of the decimal point?

How many digits long is the repeating block of the decimal expansion of 99/222

 Oct 30, 2020
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1 - 11 /37 =0.2972972972972972972972972972972972972972 =236

 

2 - 1/148 =0.00675675675675675675675675675676.......etc. [2016 -2] mod 3 =1, which means the 2016th digit is the first digit of repeating triplets of "675" = 6

 

3 - 99 / 222 =0.44594594594594594594594594594595.....etc. After the first 4 to the right of the decimal, the "repeating block" is 459, or size 3, sometimes called "the period".

 Oct 30, 2020

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