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Find the 291st digit past the decimal point in the expansion of \(\frac{1}{39}\)

 Jan 22, 2022
 #1
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\(1 \over 39\) is equal to \(0.0\overline{256410}\)

 

Digits 2, 8, and 14 are all equal to 2. By dividing, the 288th digit is 2. This means that the 291st digit is 4.

 Jan 22, 2022
 #2
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1/39 ==0.025641  025641  025641  025641  025641

 

Since the fraction has a "period" of 6, or repeating the same 6 digits, therefore the 291st digit should be:

 

291 mod 6==3, or the 3rd digit from the decimal point, or 5.

 Jan 23, 2022

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