Question

How do you convert 4/15 to a decimal?

Answer 1

The decimal form of `4/15` is `0.2bar6`.

Explanation:

Divide the numerator by the denominator.

`4/15=`

`0.2666...=`

`0.2bar(6)`

In the United States, the repeating decimal is represented with a bar above the repeating decimal. The bar has a fancy name called a vinculum, which I've never heard anyone use. Different countries have different conventions. You can read about it at https://en.m.wikipedia.org/wiki/Repeating_decimal

Answer 2

Assuming you do not have a calculator and you need to solve this manually. The explanation takes longer than doing the maths.

`0.26bar6`

Explanation:

Using an example: note that the bar in `0.33bar(3)` means that the 3 repeats for ever

With some question you are left with no choice and have to do a division.

However, this question is one where you can use a `ul("sort of cheat method")` thus avoiding doing any long division. It's all about using what you already know.

Note that `2xx15=30`. We also now that `1/3=0.333...` where the 3's just keep on repeating for ever. Perhaps we can use this.

`ul("Lets have a play!")`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)(4/15color(red)(xx1)color(white)("d")->color(white)("d")4/15 color(red)(xx2/2)=8/30)`

`8/30` is the same as `8xxubrace(1/3)xx1/10`
`color(white)("dddd.ddddddddddddd")uarr`
`color(white)("dddddddddddddddd")0.333bar3" we know this bit"`

`8xx0.333bar3xx1/10`

Just dealing with the `8xx0.333bar3` bit first

`0.333bar3`
`ul(color(white)("dddd")8 larr" Multiply")`
`color(white)("") 2.666......`

Now we deal with the `xx1/10` bit

`2.666...xx1/10=0.2666...`

Using the standard abbreviation we have:

`0.26bar6`