Question
Explain how you can tell the difference between a rational number and an irrational number.
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Answer
make it shoter
Answered by
GPT 3.5
A rational number can be expressed as a fraction, where both the numerator and the denominator are integers. For example, 2/3 is a rational number because 2 and 3 are integers. In addition, a rational number can also be written as a terminating decimal (a decimal number that has a finite number of digits after the decimal point) or a repeating decimal (a decimal number that has a repeating pattern of digits after the decimal point). For example, 0.5, 0.666..., and 1.232323... are all rational numbers.
On the other hand, an irrational number cannot be expressed as a fraction, and its decimal representation neither terminates nor repeats. Irrational numbers are often represented by non-repeating and non-terminating decimal expansions. Some examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler's number).
To distinguish between a rational and an irrational number, one can attempt to write the number as a fraction. If successful, the number is rational; otherwise, it is irrational. Another way is to examine the decimal representation of the number. If the decimal terminates or has a repeating pattern, it is rational; if it doesn't, it is irrational.
On the other hand, an irrational number cannot be expressed as a fraction, and its decimal representation neither terminates nor repeats. Irrational numbers are often represented by non-repeating and non-terminating decimal expansions. Some examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler's number).
To distinguish between a rational and an irrational number, one can attempt to write the number as a fraction. If successful, the number is rational; otherwise, it is irrational. Another way is to examine the decimal representation of the number. If the decimal terminates or has a repeating pattern, it is rational; if it doesn't, it is irrational.
Answered by
GPT 3.5
A rational number can be written as a fraction or a decimal that either terminates or repeats. An irrational number cannot be expressed as a fraction and has a decimal representation that neither terminates nor repeats.