1. What is a Terminating Fraction?

A terminating fraction is a fraction whose decimal representation ends after a finite number of digits. This occurs when the denominator (after simplifying the fraction) has no prime factors other than 2 or 5.

2. How Does the Calculator Work?

The calculator checks the denominator's prime factors:

Where:

• \( a \) — Non-negative integer (can be zero)
• \( b \) — Non-negative integer (can be zero)

Explanation: The decimal system is based on 10 (2×5), so only denominators that divide some power of 10 will terminate.

3. Importance of Terminating Fractions

Details: Terminating decimals are important in exact calculations, computer representations, and when precise decimal values are needed without rounding or repeating patterns.

4. Using the Calculator

Tips: Enter any positive integer numerator and denominator. The calculator will first simplify the fraction, then check the denominator's prime factors.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between terminating and repeating decimals?
A: Terminating decimals end (like 0.5), while repeating decimals have an infinite repeating pattern (like 0.333...).

Q2: Are all fractions with denominators of 2 or 5 terminating?
A: Yes, and any product of powers of 2 and 5 (like 8, 10, 16, 20, 25, etc.).

Q3: What about fractions that simplify to denominators of 2 or 5?
A: The calculator first simplifies the fraction, then checks the denominator. So 2/4 would be treated as 1/2 (terminating).

Q4: Is 1/1 considered terminating?
A: Yes, whole numbers are considered terminating decimals (they end after the decimal point).

Q5: Why does this matter in computing?
A: Terminating decimals can be represented exactly in binary floating-point, while repeating decimals often have rounding errors.