+0

# Decimals

0
127
2

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

Jan 22, 2022

#1
+2455
+1

$$1 \over 39$$ 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
0

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