Which number is a rational terminating decimal? sqrt 12, sqrt 39, 1/3, 5/11, 7/8

1 answer

A rational terminating decimal is a decimal that ends after a finite number of digits. Only fractions in their simplest form where the denominator has only the prime factors 2 and/or 5 will result in terminating decimals.

Let's examine the given numbers:

  1. sqrt(12): This simplifies to \(2\sqrt{3}\) and is an irrational number.
  2. sqrt(39): This is also an irrational number since 39 is not a perfect square.
  3. 1/3: This is a rational number, but its decimal representation is \(0.333...\), which is a repeating decimal (not terminating).
  4. 5/11: This is a rational number, but its decimal representation is \(0.454545...\), which is also repeating (not terminating).
  5. 7/8: This is a rational number. The decimal representation is \(0.875\), which is a terminating decimal.

Therefore, the only number among those listed that is a rational terminating decimal is 7/8.