Question

Select all the rational numbers.
56

11−−√

6.565656…

0.23

0.32416…

−538

Answer 1

Rational numbers: 56, 6.565656…, 0.23, −538.

Reasons:
- 56 and −538 are integers, hence rational (56 = 56/1, −538 = −538/1).
- 0.23 is a terminating decimal = 23/100, so rational.
- 6.565656… = 6.\overline{56} is repeating; as 650/99, so rational.

Not rational:
- √11 is irrational.
- 0.32416… (given with no repeating pattern) is a nonterminating, nonrepeating decimal, so irrational.