1. Which of these numbers can be classified as both real and irrational?
A. 5.85
B. 63.4
C. Square Root: 21
D. Square Root: 36
2. Which is an integer?
A. 23
B. 1/4
C. Square Root: 27
D. 3.402538
3. Which of these numbers is classified as a rational number?
A. Square Root: 17
B. Square Root: 23
C. Square Root: 9
D. Square Root: 2
4. Which statement is false?
A. The number zero is a rational number.
B. Some irrational numbers are also rational numbers.
C. Every irrational number is a real number.
D. Every integer is a rational number.
I dont understand any of this
1. The number that can be classified as both real and irrational is:
C. Square Root: 21
To determine this, we need to know the characteristics of real and irrational numbers. Real numbers are any number that can be found on the number line, including integers, fractions, decimals, and irrational numbers. Irrational numbers are numbers that cannot be expressed as fractions and have an infinite number of non-repeating decimal places. The square root of 21 is an irrational number because it cannot be expressed as a fraction, and its decimal representation is non-repeating.
2. The integer among the options is:
A. 23
An integer is a whole number without any fractions or decimals. It can be positive, negative, or zero. Among the given options, 23 is the only whole number, making it an integer.
3. The rational number among the options is:
C. Square Root: 9
A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. The square root of 9 is 3, which can be expressed as 3/1. Therefore, the square root of 9 is a rational number.
4. The false statement is:
B. Some irrational numbers are also rational numbers.
This statement is false because irrational numbers and rational numbers are mutually exclusive. A rational number can be expressed as a fraction, while an irrational number cannot. Therefore, there is no overlap between the two categories.
1. To determine which of the numbers can be classified as both real and irrational, we first need to understand what these terms mean.
- Real numbers are numbers that can be expressed on the number line. They include whole numbers, decimals, and fractions.
- Irrational numbers are numbers that cannot be expressed as a fraction and have an infinite number of non-repeating decimal places.
Now, let's evaluate each option:
A. 5.85: This number is a decimal, and it can be expressed as a fraction (e.g., 117/20). Hence, it is a rational number, not irrational.
B. 63.4: Similar to option A, this number is a decimal that can be expressed as a fraction (e.g., 127/2). It is a rational number, not irrational.
C. Square Root: 21: The square root of 21 cannot be expressed as a fraction or a repeating decimal. Therefore, it is an irrational number.
D. Square Root: 36: The square root of 36 can be expressed as a whole number (6). Hence, it is a rational number, not irrational.
Therefore, the correct answer is C. Square Root: 21, because it is both real and irrational.
2. An integer is a whole number (both positive and negative) or zero. To determine which option is an integer:
A. 23: This is a whole number, so it is an integer.
B. 1/4: This is a fraction, not a whole number. Therefore, it is not an integer.
C. Square Root: 27: The square root of 27 is not a whole number, so it is not an integer.
D. 3.402538: This is a decimal, not a whole number. Hence, it is not an integer.
Therefore, the correct answer is A. 23, which is an integer.
3. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers, and the denominator is not zero. Let's evaluate each option:
A. Square Root: 17: The square root of 17 cannot be expressed as a fraction, so it is an irrational number.
B. Square Root: 23: Similar to option A, the square root of 23 is an irrational number.
C. Square Root: 9: The square root of 9 is 3, which is a whole number. Hence, it is a rational number.
D. Square Root: 2: The square root of 2 is an irrational number.
Therefore, the correct answer is C. Square Root: 9, which is a rational number.
4. To identify the false statement, let's evaluate each option:
A. The number zero is a rational number: This statement is true because zero can be expressed as a fraction (e.g., 0/1).
B. Some irrational numbers are also rational numbers: This statement is true. An example is the square root of 4, which is 2.
C. Every irrational number is a real number: This statement is true. All irrational numbers lie on the real number line.
D. Every integer is a rational number: This statement is true. Every integer can be expressed as a fraction with a denominator of 1.
Therefore, the false statement is not present among the given options.