Questions: Which sets does 4.333... belong to? rational and real numbers irrational and whole numbers rational and natural numbers integers and irrational numbers

Solution Steps

To determine which sets the number \(4.333\ldots\) (which is a repeating decimal) belongs to, we need to classify it based on the properties of different number sets:

1. Rational Numbers: Numbers that can be expressed as a fraction of two integers. Repeating decimals are considered rational.
2. Real Numbers: All numbers that can be found on the number line, including both rational and irrational numbers.

Given that \(4.333\ldots\) is a repeating decimal, it is a rational number. Since all rational numbers are also real numbers, \(4.333\ldots\) belongs to both the rational and real number sets.

The number \(4.333\ldots\) is a repeating decimal, which can be expressed as the fraction \(\frac{13}{3}\). Since it can be represented as a fraction of two integers, it is classified as a rational number.

All rational numbers are also real numbers. Therefore, \(4.333\ldots\) belongs to both the set of rational numbers and the set of real numbers.

Based on the classifications, we conclude that \(4.333\ldots\) belongs to the following sets:

• Rational Numbers: \( \mathbb{Q} \)
• Real Numbers: \( \mathbb{R} \)

Final Answer