Yes, recurring numbers are rational.
What are recurring numbers?
Recurring numbers are numbers that have a repeating pattern of digits after the decimal point. For example, 1/3 is a recurring number because it can be written as 0.3333... where the '3' repeats infinitely.
What are rational numbers?
Rational numbers are numbers that can be expressed as a fraction of two integers. For example, 1/2, 3/4, and 5/7 are all rational numbers.
How are recurring numbers rational?
Recurring numbers can be expressed as fractions, making them rational. Here's how:
- Example: Let's take the recurring number 0.3333...
- We can represent this number as 'x': x = 0.3333...
- Multiplying both sides by 10, we get: 10x = 3.3333...
- Subtracting the first equation from the second, we get: 9x = 3
- Solving for x, we find: x = 3/9 = 1/3, which is a fraction of two integers.
Therefore, recurring numbers are rational because they can be expressed as a fraction of two integers.
