Question

How do you write -5/8 as a decimal?

Answer 1

`-0.625`

Explanation:

`color(blue)("Introduction to a way of thinking about this problem")`
As the 5 is less than 8 it may gives you a problem.

What follows is a bit of a cheat (not really)

Using the principle that we can change the 5 or any other number any way we wish as long as we include a way to turn the change back to its original value.

If we so wished we could change it as follows:

As given: `5/8->5xx1/8`

`=50xx1/10xx1/8`

`=500xx1/100xx1/8`

`=5000xx1/1000xx1/8`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Ignoring the negative for now.

You accumulate the adjustment in this approach

`color(green)("5 is less than 8 so change it to 50")`

`50xx1/8=color(magenta)(6)" remainder 2 "`

`color(green)("2 is less than 8 so change it to 20")`

`20xx1/8=color(magenta)(2)" remainder 4 "`

`color(green)("4 is less than 8 so change it to 40")`

`40xx1/8=color(magenta)(5)" remainder 0"`

Putting our numbers together we have `color(magenta)(625)`
................................................................................................

`color(white)()`

However, we had `color(green)("3 adjustments")` so we multiply by three lots of `1/10` to bring it back to the value it should be.

`625xx1/10xx1/10xx1/10" = "0.625`

Putting the negative back in we have `-0.625`

Answer 2

The same thing as the other solution but a neater presentation.

-0.625

Explanation:

For now forget about the negative. We can out it back at the end

Write 5 as `50xx1/10`

Start point `->50xxcolor(green)(1/10)`
`color(magenta)(6)xx8 ->color(white)("dddd")ul(48larr" Subtract")`
`ul(color(white)(~~~~~~~~~.)2 color(white)(~~~~~~~~~))`

`color(white)("d")`
`color(white)("~~~~~~~~~~~~.")20xxcolor(green)(1/10)larr" remainder of 2 changed"`
`color(magenta)(2)xx8->color(white)("dddd")ul(16larr" Subtract")`
`ul(color(white)("dddddddddddd")4color(white)("ddddddddddd"))`

`color(white)("d")`
`color(white)("ddddddddddd")40xxcolor(green)(1/10) larr" Remainder of 4 changed"`
`color(magenta)(5)xx8->color(white)("dddd")ul(40larr" Subtract")`
`color(white)("dddddddddddd")0 larr" Stop"`

So for just the numbers we have:

`color(white)("d")`
`color(magenta)(625)color(green)(xx1/10xx1/10xx1/10)`

`color(magenta)(0.625)`

Now we put the 'negative state' back giving

`color(magenta)(-0.625)`