Which expressions represent rational numbers? Check all that apply.
Rational numbers are a fundamental concept in mathematics, encompassing numbers that can be expressed as a fraction of two integers. Unlike irrational numbers, which cannot be expressed as a fraction, rational numbers are integral to various mathematical operations and real-world applications. In this article, we will explore different types of expressions to determine which ones represent rational numbers.
Firstly, let’s consider the simplest form of rational numbers: fractions. A fraction is a ratio of two integers, where the numerator (the top number) and the denominator (the bottom number) are both whole numbers. For example, 3/4, 5/2, and 10/3 are all rational numbers because they can be expressed as a fraction of two integers. Therefore, the expression “3/4” is a rational number.
Secondly, whole numbers are also rational numbers. This is because a whole number can be represented as a fraction with a denominator of 1. For instance, the number 7 can be written as 7/1, which is a rational number. Hence, the expression “7” is a rational number.
Moreover, integers, which include both positive and negative whole numbers, are also rational numbers. This is because they can be expressed as a fraction with a denominator of 1. For example, -5 can be written as -5/1, which is a rational number. Therefore, the expression “-5” is a rational number.
However, not all expressions represent rational numbers. Let’s consider decimal numbers. While some decimal numbers, such as 0.25 and 1.5, can be expressed as a fraction of two integers (1/4 and 3/2, respectively), others cannot. For instance, the decimal number 0.3333… (repeating) cannot be expressed as a fraction of two integers, making it an irrational number. Therefore, the expression “0.3333…” is not a rational number.
In conclusion, which expressions represent rational numbers? Check all that apply:
1. 3/4 (fraction)
2. 7 (whole number)
3. -5 (integer)
4. 0.25 (decimal number)
5. 0.3333… (repeating decimal)
By understanding the different forms of rational numbers and their characteristics, we can better grasp the concept and apply it in various mathematical scenarios.