Making a century

The number 100 can be written as

\[\large a + \frac{\overline{bcdef}}{\overline{ghi}} \] where \(a,b,c,d,e,f,g,h,i \) are distinct integers from 1 to 9 (not necessarily in that order).

Find the value of \(\overline {abcdefghi}\).


Source: Shakuntala Devi's Puzzle to puzzle you
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