Which expression represents a rational number?
Rational numbers are a fundamental concept in mathematics, playing a crucial role in various mathematical operations and real-world applications. In this article, we will explore different expressions that represent rational numbers and understand their significance in the field of mathematics.
Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. This means that a rational number can be written in the form of p/q, where p and q are integers, and q is not equal to zero. The expression p/q is called a fraction, and it represents a rational number.
One of the simplest expressions that represent a rational number is a whole number. For example, the number 5 can be written as 5/1, where the numerator (5) is an integer, and the denominator (1) is also an integer. Since the denominator is not zero, 5/1 is a rational number.
Another example of an expression representing a rational number is a mixed number. A mixed number consists of an integer part and a proper fraction. For instance, the mixed number 3 1/2 can be written as 7/2. Here, the integer part (3) is multiplied by the denominator (2) and added to the numerator (1), resulting in the rational number 7/2.
Decimal numbers can also represent rational numbers. A terminating decimal, which has a finite number of digits after the decimal point, is always a rational number. For example, the decimal 0.75 can be written as 75/100, which simplifies to 3/4. This fraction represents a rational number.
On the other hand, non-terminating decimals, which have an infinite number of digits after the decimal point, may or may not represent rational numbers. For instance, the decimal 0.333… (where the 3s continue indefinitely) is a rational number, as it can be written as 1/3. However, some non-terminating decimals, such as the square root of 2 (1.41421…), are irrational numbers and cannot be expressed as a fraction of two integers.
In conclusion, various expressions can represent rational numbers, including whole numbers, fractions, mixed numbers, and terminating decimals. Understanding the different forms of rational numbers is essential for mastering mathematical operations and solving real-world problems. By recognizing and working with rational numbers, we can appreciate their significance in the world of mathematics and beyond.
