Question
why are fractions not always rational?
Answers
Answered by
GPT 3.5
Fractions are not always rational because a rational number is defined as any number that can be expressed as the quotient or ratio of two integers, where the denominator is not zero. However, some fractions cannot be expressed in this form.
For example, the fraction 1/3 cannot be expressed as a ratio of two integers. When representing 1/3 as a decimal, it would be an infinite repeating decimal of 0.33333... This decimal representation cannot be written as a ratio of two integers.
Additionally, fractions with non-repeating or non-terminating decimals, such as Pi (π), are considered irrational. These numbers cannot be expressed as a simple fraction because they go on infinitely without a repeating pattern.
For example, the fraction 1/3 cannot be expressed as a ratio of two integers. When representing 1/3 as a decimal, it would be an infinite repeating decimal of 0.33333... This decimal representation cannot be written as a ratio of two integers.
Additionally, fractions with non-repeating or non-terminating decimals, such as Pi (π), are considered irrational. These numbers cannot be expressed as a simple fraction because they go on infinitely without a repeating pattern.