A rational number is any number that can be expressed as the quotient of two integers (a fraction), where the denominator is not zero.
Let's evaluate the numbers you've provided:
-
7.6 - This is a decimal, but it can be expressed as the fraction 76/10, which simplifies to 38/5. Therefore, it is rational.
-
22/7 - This is already in the form of a fraction, where both the numerator (22) and the denominator (7) are integers. Therefore, it is rational.
-
3.14 - This is another decimal, but it can be approximated by the fraction 314/100. Although it is often treated as a rational number due to its finite decimal representation, it is important to note that it is not an exact representation of the mathematical constant π. However, it can still be classified as rational.
-
1.01 repeating (denoted as 1.011111...) - This is a repeating decimal and can be expressed as a fraction. Specifically, it can be represented as \( \frac{101}{99} \). Therefore, it is also rational.
In conclusion, all the given numbers are rational. So, the correct selections are:
- 7.6
- 22/7
- 3.14
- 1.01 repeating
2 answers