Question

How do you write `3/7` as a decimal?

Answer 1

`3/7 = 0.bar(428571)`

Explanation:

Long divide `3` by `7` to find `3/7 = 0.bar(428571)`

Long divide until the remainder repeats. In this case we find the remainder `3`, repeating the number we started with.

This show us that the pattern `428571` will repeat, so we write:

`3/7 = 0.bar(428571)`

or with dots:

`3/7 = 0.dot(4)2857dot(1)`

Answer 2

`0.bar(428571)`

Explanation:

The sevenths' decimals have an interesting property: they repeat with the same numbers, in the same order.

The decimals of any fraction with denominator `7` have the digits in order:

`1,4,2,8,5,7`

For example,

`1/7=0. color(red)(142857)color(green)(142857)color(blue)(142857)...=0.bar(152857)`

`2/7` follows the same pattern, except for that it starts with the next highest number in the series `1,4,2,8,5,7`, which is `2`. The decimal then goes in order, up until `7`, then goes to `1,4` at the beginning and beings the series again:

`2/7=0. color(red)(285714)color(green)(285714)color(blue)(285714)...=0.bar(285714)`

`3/7` behaves similarly, except for that it begins with the next highest number -- `4`.

`3/7=0. color(red)428571color(green)428571color(blue)425871 ... = 0.bar(428571)`

The series continues:

`4/7=0.bar571428`

`5/7=0.bar714285`

`6/7=0.bar857142`