Final answer:
A rational number is a quotient of two integers; an irrational number cannot be expressed as a simple fraction. Numbers that are whole, fractions, or repeating decimals are rational, such as 5.012121212 (repeating), 400, 1000, 3/30, and − 250/5.
Step-by-step explanation:
To determine whether a number is rational or irrational, one must recognize that a rational number is any number that can be expressed as the quotient or fraction ⅓ of two integers, with the denominator not being zero. An irrational number is a number that cannot be expressed as a simple fraction; it's decimal goes on forever without repeating. A repeating decimal or a fraction represents a rational number.
1. The number 5.012121212... is rational because it has a repeating pattern (1212...). 2. The number 400 (assuming it's meant as a whole number) is rational because it can be written as a fraction, ⅓ 400/1. 3. The number 1000 is rational for the same reason, represented as 1000/1. 4. The fraction 3/30 is rational because it is already in fraction form and can be reduced to 1/10. 5. The number − 250/5 is rational; it's just − 50 when simplified. 6. Whether 0.01562138411 is rational or irrational cannot be determined without knowing whether the digits after the decimal point repeat or terminate; if they do not repeat and are not terminating, it would be irrational.