Numbers 13 and -142 are classified as rational because they can be written as fractions. The number 0.325 is also rational due to its finite decimal representation. However, 0.4562345... and the square root of 50 are classified as irrational, as their decimals do not terminate or repeat and the square root of 50 can't be expressed precisely as a fraction.
To classify each number as rational or irrational, we need to understand the definitions of these terms. A rational number is any number that can be expressed as a fraction or ratio of two integers (where the denominator is not zero), which includes all integers, finite decimals, and repeating decimals. An irrational number is a number that cannot be expressed as a simple fraction; its decimal goes on forever without repeating.
- 13 is a whole number, and since it can be expressed as the fraction 13/1, it is rational.
- 0.325 is a decimal with a finite number of digits, so it can be written as a fraction (325/1000), making it rational.
- 0.4562345... with the '...' indicating that the digits continue indefinitely without a pattern, suggests it is irrational.
- √50 (the square root of 50) cannot be simplified to an exact fraction, and since 50 is not a perfect square, √50 is considered irrational.
- −142 is an integer and can be written as a fraction (-142/1), so it is rational.