Question

How do you write `4 1/3` as a decimal? Use bar notation if the decimal is a repeating decimal.

Answer 1

`4.bar(3)`

Explanation:

`4(1/3)= 13/3`

`13/3= 4.bar3`

Answer 2

`4.bar33`

Explanation:

There are a couple things you could do:

Example 1:
Change the mixed fraction to an improper fraction.

Multiply the denominator and whole number,

`3 xx 4 = 12`

Take that answer and add the numerator,

`12 + 1 = 13`

Now put that answer over the denominator,

`13/3`

Next step is to divide `3` into `13`.

`color(white)( (3)/color(black)(3)) color(white)( (color(black)(4.33)))/( ")" 13.00) ""`
`color(white)(xx)(12)/color(white)`
`color(white)(xxxii)1(0)->`bring down 0 (it becomes 10)`color(white)`
`color(white)(xxxxi)9/ color(white)`
`color(white)(xxxxx)1 ->`It will continue to repeat##

Since `4.33` is a repeating decimal, you would write it with a bar.

`4.bar33`

Example 2:
Write `4 1/3` as an expression.

`4 + 1/3`

Divide `1/3` the same way as above,

`color(white)( (1)/color(black)(3)) color(white)( (color(black)(0.33)))/( ") 1.00 ""`

Now that you know `1/3` is `0.bar33`, add the whole number from the fraction,

`4 + 0.bar33 = 4.bar33`

A third way, and probably the easiest way, is to use a calculator. However, if you need to show work use the examples above.