Question

What is the repeating decimal patternfor fractions with a denominator of 13?

Answer 1

what is \(\frac{1}{13}\)?

Answer 2

0.076923076923.......

Answer 3

\[x=\frac 1{13}=0.07692307692307693....\]\[\quad=0.0\dot769230\dot7\]
\[1000000x=76923.0\dot769230\dot7\]
\[999999x=76923\]
\[x=\frac{76923}{999999}\]
\[\frac 1{13}=\frac{76923}{999999}\]
\[\frac n{13}=n\frac{76923}{999999}\]

Answer 4

repeating decimal is that___
1/13=0.076923076923076923

Answer 5

that is 0.076923

Answer 6

@yociyoci

Answer 7

but i am trying to find the decimal pattern for any fractions with the denominator of 13, like 1/13 = 0.076923076923 and 2/13 = 0.153846153846 and 3/13= 0.230769230769

by analyzing these, how do you find the pattern for the next ones?

Answer 8

by multiplying 0.076923 by number what you want like 9/13=?
then you would multiply 0.076923 by 9 to get =9/13

Answer 9

@yociyoci

Answer 10

9/13 = 0.692307 whole bar... on 692307 not on 0

Answer 11

so there isn't a number pattern to the decimal from 1/13 to 12/13?

Answer 12

there is a pattern

Answer 13

Can you please clarify?

Answer 14

yaaa!! there is a pattern that multiply 0.076923 by 12 to get =12/13

Answer 15

ok, sure

Answer 16

thx

Answer 17

welcome...