Are All Decimals Irrational Numbers?
No, not all decimals are irrational numbers. In fact, most decimals are rational numbers. Let's break down the difference:
Rational Numbers
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers and the denominator is not zero. These fractions can be represented as terminating or repeating decimals.
Examples of rational numbers:
- Terminating decimals: 0.5, 2.75, 10.00
- Repeating decimals: 0.333..., 1.234234..., 0.142857142857...
Irrational Numbers
An irrational number is a number that cannot be expressed as a fraction of two integers. Their decimal representations are non-repeating and non-terminating.
Examples of irrational numbers:
- Pi (π): 3.1415926535...
- Square root of 2 (√2): 1.41421356...
- Euler's number (e): 2.718281828...
Key Takeaways
- Rational numbers: Can be expressed as fractions, have terminating or repeating decimals.
- Irrational numbers: Cannot be expressed as fractions, have non-repeating and non-terminating decimals.
Therefore, not all decimals are irrational numbers. Only those with non-repeating and non-terminating decimals are considered irrational.
