Question

How do you express `84/162` in decimal to `3` decimal places ?

Answer 1

`84/162 = 14/27 = 0.bar(518) ~~ 0.519`

Explanation:

First find the greatest common factor (GCF) of `84` and `162`.

We can find the GCF of two numbers as follows:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is `0` then the smaller number is the GCF.

• Otherwise repeat with the smaller number and the remainder.

So in our example:

`162/84 = 1" "` with remainder `78`

`84/78 = 1" "` with remainder `6`

`78/6 = 13" "` with remainder `0`

So the GCF of `162` and `84` is `6`.

So:

`84/162 = (84-:6)/(162-:6) = 14/27`

which is in lowest terms.

Note that `27*37 = 999`

Hence:

`1/27 = 37/999 = 0.bar(037)`

and:

`14/27 = (14*37)/999 = 518/999 = 0.bar(518)`

Rounded to `3` decimal places:

`14/27 ~~ 0.519`

since the digit after `8` is `5 >= 5`.