Write the number

$4\mathrm{.}921=4\mathrm{.}9212121...$

as a ratio of integers.

Solution

$4\mathrm{.}9212121=4\mathrm{.}9+$

$21103$

$+$

$21105$

$+$

$21107$

$+$

After the first term we have a geometric series with

a $=$

$21103$

and

r $=.$

Therefore we have the following.

$4\mathrm{.}921=4\mathrm{.}9+$

$21103$

$1$

$=4\mathrm{.}9+$

$211000$

$99100$

$=$

$49$

$+$

$990$

$=$