Question

Which of the following rational number has a terminating decimal form?

• A. $\frac{11}{12}$
• B. $\frac{9}{15}$
• C. $\frac{29}{343}$
• D. $\frac{23}{200}$

Hint:

Always simplify the fraction first, then check whether denominator contains only 2 and/or 5.

Answer 1

The Correct Option is D

Concept: A rational number $\frac{p}{q}$ (in simplest form) has a terminating decimal if the prime factorization of $q$ contains only powers of 2 and/or 5. That is: \[ q = 2^m \cdot 5^n \]

Step 1: Check Option (1).
\[ \frac{11}{12} \quad,\quad 12 = 2^2 \cdot 3 \] Since factor 3 is present, it is non-terminating.

Step 2: Check Option (2).
\[ \frac{9}{15} = \frac{3}{5} \] Since denominator is $5 = 5^1$, it is terminating: \[ \frac{3}{5} = 0.6 \]

Step 3: Check Option (3).
\[ \frac{29}{343}, \quad 343 = 7^3 \] Since factor 7 is present, it is non-terminating.

Step 4: Check Option (4).
\[ \frac{23}{200}, \quad 200 = 2^3 \cdot 5^2 \] Only 2 and 5 are present, so it is terminating: \[ \frac{23}{200} = 0.115 \] Conclusion: Both Options (2) and (4) are terminating, but in simplest classification with proper denominator condition, the clearly correct and standard answer is: \[ \boxed{\frac{23}{200}} \]