Exploring the Rationality of the Number 47- A Deep Dive into the World of Rational Numbers
Is 4/7 a Rational Number?
Rational numbers are an integral part of mathematics, representing numbers that can be expressed as a fraction of two integers. The question “Is 4/7 a rational number?” is a fundamental inquiry that delves into the nature of rationality in the realm of numbers. To answer this question, we must first understand what constitutes a rational number and then evaluate whether 4/7 fits the criteria.
A rational number is defined as any number that can be written in the form of a fraction, where both the numerator and the denominator are integers, and the denominator is not equal to zero. In other words, a rational number can be expressed as p/q, where p and q are integers and q ≠ 0. This definition allows us to categorize numbers into rational and irrational categories.
In the case of 4/7, the numerator is 4 and the denominator is 7. Both 4 and 7 are integers, and 7 is not equal to zero. Therefore, 4/7 can be written as a fraction with integer numerator and denominator, which means it is a rational number.
Moreover, the decimal representation of 4/7 also supports its classification as a rational number. When dividing 4 by 7, the decimal expansion terminates, indicating that the number is rational. In this case, 4/7 is equal to 0.5714285714285714… (the pattern 571428 repeats indefinitely), which is a terminating decimal. This further confirms that 4/7 is a rational number.
In conclusion, the question “Is 4/7 a rational number?” can be answered with a resounding yes. 4/7 meets the criteria of being a rational number as it can be expressed as a fraction with integer numerator and denominator, and its decimal representation is a terminating decimal. Understanding the nature of rational numbers is crucial in various mathematical concepts and applications, and recognizing 4/7 as a rational number is an essential step in this understanding.
