Math

Terminating Decimals Calculator

Check whether a fraction gives a terminating decimal.

Calculated Output

Terminates? yes

Decimal value 0.375

Formula: Terminates ⟺ reduced denominator factors only into 2s and 5s

Step-by-Step Breakdown

1. Values used:

2. Numerator = 3

3. Denominator = 8

5. Terminates? = yes

6. Decimal value = Numerator / Denominator = 3 / 8 = 0.375

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The math behind it

Reduce the fraction, then factor the denominator. If the only prime factors are 2 and 5, the decimal terminates; otherwise it repeats.

3/8 = 0.375 terminates (8 = 2³); 1/3 = 0.333… repeats.

Why 2 and 5?

Because they are the prime factors of 10, the base of our decimal system.