# What is 1 8/9 as a decimal?

May 30, 2017

$1 \frac{8}{9} = 1.88888 . = 1. \overline{8}$

#### Explanation:

When we have a denominator in a fraction, which in its smallest form and has as its factors prime numbers other than $2$ and $5$, you can not write the fraction as a termiinating decimal .

In such cases, we get repeating decimals. This is also true in this case as $9$ has its prime factor $3$.

Dividing $8$ by $9$ using long division, we get

$\text{ "0.8" "8" "8" "8" "8" } 8$

9" ")bar(8.0" "0" "0" "0" "0" "0)
$\text{ "ul(72)" } \downarrow$
$\text{ "8" } 0$
" "ul(7" "2)
$\text{ "8" } 0$
" "ul(7" "2)
$\text{ "8" } 0$
" "ul(7" "2)
$\text{ "8" } 0$

...

...

Hence $\frac{8}{9} = 0.88888 \ldots \ldots$

and $1 \frac{8}{9} = 1.88888 \ldots \ldots$

which wecan also write as $1. \overline{8}$, which shows $8$ repeats endlessly.