Math Problem : G.7 Decimals to be represented by fraction

Represent 0.214214214214 -------- by a fraction.

Answer

214/999

Solution

0.214214214… × 1000 = 214.214214214…
214.214214214...... - 0.214214214214… = 214.　
214 = 0.214214214214… × (1000 -1 ) = 0.214214214214… × 999
Therefore, 0.214214214214…　＝ 214/999.