Final answer:
Rational numbers can be expressed as fractions with integers, while irrational numbers have non-repeating, non-terminating decimals and cannot form such fractions. The numbers: 2.8, 2/3, -3, 4/5, -1/2, 4/5, 7, and √36 are rational; whereas √7 and -√2 are irrational.
Step-by-step explanation:
To determine if the following numbers are rational or irrational: 2.8, 2/3, -3, 4/5, -1/2, 4/5, √7, 7, √36, -√2, we need to understand the difference between rational and irrational numbers. A rational number is any number that can be expressed as a fraction ∕, where both 'p' and 'q' are integers and 'q' is not equal to zero. An irrational number cannot be expressed as a simple fraction and has non-repeating, non-terminating decimal components.
- 2.8 is a rational number because it can be written as 28/10 or 14/5.
- 2/3 is a rational number as it's already in fraction form.
- -3 is rational because it can be expressed as -3/1.
- 4/5 is rational, already in fraction form.
- -1/2 is rational, already in fraction form.
- 4/5 (repeated) is rational, already in fraction form.
- √7 is irrational because it cannot be expressed as a fraction of two integers and its decimal form is non-terminating and non-repeating.
- 7 is rational because it can be expressed as 7/1.
- √36 is rational because it equals 6, which can be written as 6/1.
- -√2 is irrational because the square root of 2 is an irrational number.
Based on the above information, the correct classification is: Rational, Rational, Rational, Rational, Rational, Rational, Irrational, Rational, Rational, Irrational.