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# math problem

0
208
2

We know that 1/13 =0.0769230769230769230769230769230769... When 1/130 is written as a repeating decimal, what is its 130th digit to the right of the decimal point?

May 31, 2021

#1
+117766
+2

1/13 =0.0769230769230769230769230769230769...

$$1/13 =0.\dot 07692307692\dot3\\$$

there are 12 repeating digits after the decimal point

130/12= 10 and 10/12

the 10 digit is 9

when you divide this number by 10 the 130th place after the decimal point  will be 6

You need to check this.

May 31, 2021
#2
+36432
+2

1/130 = .0 076923 076923......

there are 6 digits that repeat after the initial 0

130/6    is 21 2/3   so

the 130 th would normally be a   '9'    ( 2/3 position of the string)   but the string is shifted one digit to the right due to the first '0'

so the 130th digit will be '6'           As Melody found in her answer ........

May 31, 2021