What will be the decimal expansion of \(\frac{29}{343}\)? 

Explanation -

we have \(\frac{29}{343}\)

The decimal expansion of 29/343 is terminating or non-terminating recurring (repeating) or non-terminating non-recurring, we need to look at the properties of the denominator when it is reduced to its prime factors.

343 can be factored as 343 = 7³ 

A fraction in its simplest form will have a terminating decimal expansion if and only if the denominator has no prime factors other than 2 and 5. Since 343 is 7³ and does not contain any factors of 2 or 5, it means the decimal expansion of 29/343 will not be terminating.

Next, to determine if it is non-terminating and recurring, we can perform the long division of 29 by 343.

When a fraction is in its simplest form and the denominator has prime factors other than 2 and 5, its decimal expansion is always non-terminating and recurring.

Hence, the correct option is (2).