identify whether the number is rational or irrational. then explain why it is rational or irrational.
8/17
and
21.192
Study this site. I'll be glad to check your answers.
http://www.mathsisfun.com/irrational-numbers.html
so the first one is rational and the second one is irrational, but i do not no how to explain why is it irrational and rational
21.192 is irrational beacues it keeps reapeating and when it keeps reapeating it is irrational.
8/17
To determine whether a number is rational or irrational, we need to understand the concepts behind each.
1. Rational number: A rational number is a number that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. Rational numbers can be either terminating or repeating decimals.
2. Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers. Irrational numbers cannot be written as terminating or repeating decimals, and their decimal representation goes on infinitely without a pattern.
Now, let's analyze the given numbers:
1. 8/17:
To determine whether 8/17 is rational or irrational, we need to check if it can be expressed as a fraction of two integers. In this case, 8/17 is a fraction, indicating that it is a rational number. Since both the numerator (8) and denominator (17) are integers, and the denominator is not zero, we can conclude that 8/17 is a rational number.
2. 21.192:
To determine whether 21.192 is rational or irrational, we need to examine its decimal representation. 21.192 is a finite decimal, with no repeating or infinite pattern. It can be expressed in fraction form as 21192/1000, which simplifies to 5298/250. Since 5298 and 250 are both integers, and the denominator is not zero, we can conclude that 21.192 is a rational number.
In summary:
- 8/17 is a rational number because it can be expressed as a fraction of two integers.
- 21.192 is also a rational number because it can be expressed as a fraction of two integers.