Write the number

$1\mathrm{.}719=1\mathrm{.}7191919...$

as a ratio of integers.

Solution

$1\mathrm{.}7191919=1\mathrm{.}7+$

$19103$

$+$

$19105$

$+$

$19107$

$+$

After the first term we have a geometric series with

a $=$

$19103$

and

r $=.$

Therefore we have the following.

$1\mathrm{.}719=1\mathrm{.}7+$

$19103$

$1$

$=1\mathrm{.}7+$

$191000$

$99100$

$=$

$17$

$+$

$990$

$=$