Provide an appropriate response.
-Convert the decimal .2949494. . . to a fraction by writing it as the infinite series $$\frac { 2 } { 10 } + \frac { 94 } { 10 \cdot 100 } + \frac { 94 } { 10 \cdot 100 ^ { 2 } } + \frac { 94 } { 10 \cdot 100 ^ { 3 } } + \ldots$$
A) 0.29494949
B) 0.29170829
C) 0.29229229
D) 0.292

Question

Quizplus · Accepted Answer

The given series represents the decimal expansion of 0.29494949... where each term adds another repetition of 94 in the decimal places, accurately reflecting the decimal given in the question.

Provide an Appropriate Response 210+9410⋅100+9410⋅1002+9410⋅1003+…\frac { 2 } { 10 } + \frac { 94 } { 10 \cdot 100 } + \frac { 94 } { 10 \cdot 100 ^ { 2 } } + \frac { 94 } { 10 \cdot 100 ^ { 3 } } + \ldots102​+10⋅10094​+10⋅100294​+10⋅100394​+…

Provide an Appropriate Response $\frac { 2 } { 10 } + \frac { 94 } { 10 \cdot 100 } + \frac { 94 } { 10 \cdot 100 ^ { 2 } } + \frac { 94 } { 10 \cdot 100 ^ { 3 } } + \ldots$