Are repeating decimals rational or irrational?
Understand the Problem
The question is asking whether repeating decimals fall under the category of rational or irrational numbers. To answer this, we need to understand the definitions of both types of numbers. Rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot be expressed in this way. Since repeating decimals can be expressed as fractions, they are considered rational.
Answer
Repeating decimals are rational numbers.
Repeating decimals are rational numbers because they can be expressed as a ratio of two integers.
Answer for screen readers
Repeating decimals are rational numbers because they can be expressed as a ratio of two integers.
More Information
Repeating decimals are considered rational because they can always be written as a fraction. This is different from irrational numbers, which cannot be expressed as a ratio of two integers.
Tips
A common mistake is to assume that non-terminating decimals are irrational. However, if a non-terminating decimal repeats, it is rational.
Sources
- Repeating Decimal - Wikipedia - en.wikipedia.org
- Why aren't repeating decimals irrational but something like π is? - Math Stack Exchange - math.stackexchange.com
- Rational and irrational numbers - Math Central - mathcentral.uregina.ca
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