Question

Express the recurring decimal 0.034 as a fraction in its simplest form.

Answer 1

Answer:

$\frac{17}{495}$ will be the fraction.

Step-by-step explanation:

Here the recurring decimal number is 0.0343434....

To convert this recurring decimal to fraction we assume,

x = 0.03434....   -------(1)

Now multiply both the sides with 100.

100x = 3.43434.... ------(2)

Now subtract equation (1) from equation (2).

100x = 3.43434

     x = 0.03434

99x = 3.4

x = $\frac{3.4}{99}$

  = $\frac{34}{990}$

x = $\frac{17}{495}$

Therefore, fraction that represents the decimal number is $\frac{17}{495}$