0.47 = (A) 43/90 (B) 47/90 (C) 49/99 (D) 47/2

Question

\(0.4\bar 7 =\)

(A) \(\frac{43}{90}\)

(B) \(\frac{47}{90}\)

(C) \(\frac{49}{99}\)

(D) \(\frac{47}{2}\) 

Answer 1

Correct option is (A) \(\frac{43}{90}\)

Let \(x=0.4 \overline{7}=0.4777\)    ......(i)

Multiplying equation (i) with 10.

\(10 x=10 \times 0.4777 \ldots\)

\(10 x=4.777 \ldots\)

Subtracting eq (ii) from (i),

\(10 x-x =4.777 \ldots-0.477 \ldots\)

\(9 x =4.300 \ldots\)

\(x =\frac{4.3}{9}\)

\(x =\frac{43}{90}\)

Thus, \(0.4 \overline{7}=\frac{43}{90}\).

Answer 2

सही विकल्प है (A) \(\frac{43}{90}\)