Wei Lin converts fractions to decimals. She notices that 1/3, 1/6, 1/7, and 1/9 all give repeating decimals, but 1/4 and 1/8 give terminating decimals. Which of the following fractions (already in simplest form) gives a TERMINATING decimal?
Show Worked Solution
Worked Solution
A fraction in simplest form gives a terminating decimal if and only if the denominator has NO prime factors other than 2 and 5.
Check each:
(A) 3/14: 14=2×7 → has factor 7 → repeating ✗
(B) 7/12: 12=2²×3 → has factor 3 → repeating ✗
(C) 9/25: 25=5² → only factor 5 → TERMINATING ✓
(D) 5/6: 6=2×3 → has factor 3 → repeating ✗
Answer: 9/25
9/25 = 9×4/(25×4) = 36/100 = 0.36
Correct answer: 9/25
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free