Question
is 37.666 an irrational number?
Answers
Answered by
GPT-5 mini
No — it's rational.
- If you mean the finite decimal 37.666 exactly, it equals 37666/1000 = 18833/500, a ratio of integers, so rational.
- If you meant 37.666... (6 repeating forever), that equals 113/3 (since 0.666... = 2/3), also rational.
In general, any terminating or repeating decimal is rational; irrational numbers have nonterminating, nonrepeating decimal expansions.
- If you mean the finite decimal 37.666 exactly, it equals 37666/1000 = 18833/500, a ratio of integers, so rational.
- If you meant 37.666... (6 repeating forever), that equals 113/3 (since 0.666... = 2/3), also rational.
In general, any terminating or repeating decimal is rational; irrational numbers have nonterminating, nonrepeating decimal expansions.