Which of these numbers can be classified as both real and rational?
(1 point)
1/2
-1.016879413894...
square root 5
0.89089908999...
The number 1/2 can be classified as both real and rational.
The number that can be classified as both real and rational is 1/2.
To determine which numbers can be classified as both real and rational, let's first understand what each term means.
1. Real numbers: Real numbers include all numbers on the number line, including integers, fractions, decimals, and irrational numbers. In other words, real numbers encompass the entire spectrum of numerical values.
2. Rational numbers: Rational numbers are a subset of real numbers that can be expressed as the ratio of two integers (p/q), where q is not equal to zero. They can be written either as terminating decimals or repeating decimals.
Now let's analyze each option:
1. 1/2: This number can be expressed as the ratio of two integers (1 and 2). Hence, it is a rational number and, therefore, real.
2. -1.016879413894...: This number is not a rational number. It appears to be an irrational number, as it does not terminate or repeat. However, we need more information to definitively conclude its classification as rational or irrational.
3. Square root of 5: The square root of 5 is an irrational number, as it cannot be expressed as the ratio of two integers. Therefore, it is real but not rational.
4. 0.89089908999...: This number appears to be a repeating decimal, indicating that it can indeed be expressed as the ratio of two integers. Thus, it is both rational and real.
In conclusion, the number 1/2 and the decimal 0.89089908999... can be classified as both real and rational numbers. The numbers -1.016879413894... and the square root of 5 are real numbers but not rational numbers.