GMAT Quant: How to Identify Terminating and Repeating Decimals?

Short Answer

A fraction terminates only if its denominator, after simplification, has no prime factors other than 2 and 5; else, it repeats. For example, 3/40 terminates because 40 = 2³ × 5. In contrast, 1/12 repeats, since 12 includes the prime factor 3.

Overview

In your GMAT preparation course, you will see how the simplest ideas often carry the greatest value. Terminating fractions illustrate this perfectly. What seems like routine arithmetic actually reveals deeper patterns once examined carefully. Determining whether a fraction ends or repeats is not about lengthy calculation but about clarity of thought. This habit of spotting structure where others see confusion strengthens your reasoning and builds confidence under time pressure. Consistent practice with GMAT practice tests helps you apply this clarity under exam-like conditions, so the approach becomes second nature and supports both accuracy and composure on test day.

 

Understanding the Concept of Terminating and Repeating Fractions

A recurring question type on the GMAT asks whether a fraction will terminate or repeat. The principle is straightforward. A fraction terminates only when the denominator, once simplified, contains no prime factors other than 2 and 5. If there is even a single occurrence of another prime number, the decimal will recur indefinitely.

Simple Examples to Build Intuition

Take 1/2. It becomes 0.5, which clearly terminates.

Similarly, 1/5 becomes 0.2, which also terminates.

However, when you take 1/3, the result is 0.333…, which never ends.

The same holds for 1/7, which becomes 0.142857 repeating endlessly.

Even if a denominator has plenty of 2s or 5s, the presence of any other prime, such as 3 or 7, prevents termination.

For example, 48 has many 2s but also a 3, so a fraction with 48 as the denominator will not terminate.

Applying the Rule to GMAT Questions

We discussed the following question in the video:

Q. Which of the following will terminate?

• • 13/37
  • 32/59
  • 83/140
  • 63/280
  • 43/480

To solve, simplify each denominator and check its prime factors.

• 37 is prime, not 2 or 5 → does not terminate.
• 59 is prime, not 2 or 5 → does not terminate.
• 140 = 2 × 2 × 5 × 7 → the 7 makes it non-terminating.
• 280 = 2³ × 5 × 7 → again, the 7 prevents termination.
• 480 = 2⁵ × 3 × 5 → at first it looks non-terminating because of the 3.

Now simplify 43/480. Cancel the common factor of 3. The fraction reduces to 43/40.

40 = 2³ × 5, which contains only 2s and 5s.

Therefore, 43/480 simplifies to a terminating fraction.

E is the correct answer.

This example shows how cancellation can completely change the denominator. Always reduce first, then apply the rule.

The Deeper Lesson for Test-Takers

This concept emphasizes the importance of looking beneath the surface. The GMAT often disguises simple truths within seemingly complex expressions. Rather than attempting to calculate decimals, a quick factorization of the denominator can save precious time and help avoid traps. Beyond the math, this habit of looking deeper and finding structure where others see chaos mirrors the kind of analytical ability valued in MBA admission evaluations, where clarity of thought often outweighs surface-level detail.

Parting Thought

The lesson of terminating fractions goes far beyond decimals. It teaches you to look past the surface and search for the structure hidden beneath. On the GMAT, it is rarely brute calculation that wins; it is the calm recognition of patterns and the discipline to simplify before acting. When you train yourself to pause and factorize, you learn to replace clutter with clarity. This is the same habit that separates strong thinkers from hurried guessers. With practice, you discover that what first seemed ordinary holds deeper meaning, shaping both your test performance and your approach to problem-solving in life.

 

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