Question

How do you convert 4.6 (6 repeating) to a fraction?

Answer 1

`4 2/3`

Explanation:

Formatting Tip: For a repeating number us the command 'bar'

So for 4.666 repeating I would write 4.66bar6. If you write this but with the hash symbol at the beginning and end you get `4.66bar6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solved by inspection")`

Known: `1/3 -> 0.3333bar3`

So `2/3 -> 0.6666bar6`

Thus `4.66bar6 = 4 2/3`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solved mathematically")`
Let `x = 4.66bar6`

Then `10x=46.66bar6`

So `10x-x= 46.66bar6`
`" "underline(" "4.66bar6color(white)(.))" subtract"`
`" "9x=42`

Divide both sides by 9

`x=42/9 = 4 2/3`