Question

Write the decimal expansion of those numbers from the following that have terminating decimals.

`17/343`

Answer 1

Let’s determine whether `17/343` has a terminating or non-terminating decimal expansion.

Step 1: Factorize the denominator

343 = 7 × 7 × 7 = 7³

Step 2: Apply the rule

A rational number `p/q` (in lowest terms) has a terminating decimal expansion if and only if the prime factors of q are only 2 and/or 5.

Here, the denominator 343 = 7³ contains prime factor 7, not 2 or 5.

Therefore, `17/343` has a non-terminating recurring decimal expansion, it does not have a terminating decimal.