Explain why 25 is rational and 26 is irrational
Asked this morning:
https://www.jiskha.com/questions/1806218/6-Explain-why-25-is-rational-and-26-is-irrational-5-points
To determine whether a number is rational or irrational, we need to understand their definitions.
A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. It implies that the number can be written as a finite or repeating decimal.
On the other hand, an irrational number cannot be expressed as a fraction or a ratio of two integers. It implies that the number has non-repeating and non-terminating decimal representation.
Now, let's apply these definitions to the numbers 25 and 26:
1. 25:
To check if 25 is rational, we need to see if it can be expressed as a fraction. In this case, 25 can be written as 25/1. Both the numerator (25) and denominator (1) are integers, so 25 is rational. Additionally, 25 can be expressed as a finite decimal, 25.0000, which further confirms it is rational.
2. 26:
To check if 26 is irrational, we need to see if it can be expressed as a fraction. In this case, 26 cannot be written as a fraction with integers in the numerator and denominator. Therefore, 26 is not rational. Furthermore, 26 cannot be expressed as a finite decimal since it would require infinite decimal places, thus making it an irrational number.
In conclusion, 25 is rational because it can be expressed as a fraction and has a finite decimal representation. On the other hand, 26 is irrational because it cannot be expressed as a fraction and has an infinite non-repeating decimal representation.