Final answer:
Numbers 1/3, 6.99999..., 7.48331, and 10 are rational because they can be expressed as a ratio of two integers or they are integers themselves, while 18π is irrational because π is an irrational number.
Step-by-step explanation:
To determine whether each number is irrational or rational, we'll review the definitions and examine each given number:
- 1/3: This is a fraction representing a division of a whole into three equal parts. Since it can be expressed as a ratio of two integers (1 and 3), it is a rational number.
- 6.99999...: The notation '...' indicates this number is repeating indefinitely. A repeating decimal is also a rational number because it can be expressed as a fraction.
- 7.48331: If this decimal terminates (does not go on forever) and has no repeating pattern, it is a rational number.
- 10: This is an integer, and all integers are rational numbers because they can be represented as a ratio of themselves and 1 (10/1).
- 18π: Pi (π) is a well-known irrational number that cannot be accurately expressed as a fraction. Multiplying an irrational number by a rational number (such as 18) results in an irrational number.
Remember to eliminate terms wherever possible to simplify the algebra and to always check the answer to see if it is reasonable.