Question

$2.\bar{56}=?$ The correct expression (bar denotes repeating decimal)

• A. $$2\frac{560}{90}$$
• B. $$2\frac{56}{99}$$
• C. $$2\frac{56}{1000}$$
• D. $$2\frac{56}{100}$$

Answer 1

Answer:

$$2\frac{56}{99}$$

Calculation:

$x=2.\bar{56}$

$=x=2.565656.....$ -----------(1)

$=100x=256.5656...$---------------(2) [eq(1)$\times$100]

Substracting eq (1) from (2), we get

$99x = 254$

$= x = \frac{254}{99}$

$=x = 2\frac{56}{99}$