1.
Which of the following numbers is not a rational number?
Correct Answer
C. √ 2
Explanation
A rational number is any number that can be expressed as a fraction (ratio) of two integers. The numbers 1/2, 0.25, and 23 are all rational because they can be written as a ratio of two integers. However, √2 is not a rational number because it cannot be expressed as a simple fraction; it is an irrational number with a nonrepeating, nonterminating decimal expansion.
2.
Which of the following numbers is irrational?
Correct Answer
C. √2
Explanation
An irrational number cannot be expressed as a simple fraction of two integers. The square root of 2 is a nonterminating, nonrepeating decimal, meaning its decimal representation goes on forever without a pattern. This makes it impossible to write as a fraction, thus making it irrational.
3.
Which number is irrational?
Correct Answer
D. 9.946787839395329
Explanation
The number 9.946787839395329. An irrational number is a real number that cannot be expressed as a fraction of two integers, and its decimal representation is nonterminating and nonrepeating. These numbers possess infinite and nonpatterned decimal expansions, challenging traditional notions of numerical representation.
4.
Pi is a rational number.
Correct Answer
B. False
Explanation
Pi (π) is an irrational number, meaning it cannot be expressed as a simple fraction or ratio of two integers. Its decimal representation is nonterminating and nonrepeating, which is a key characteristic of irrational numbers. While approximations of Pi (like 22/7) are used in calculations, Pi itself is not a rational number.
5.
All of the following numbers are rational.

1/6

.425

1

1,234,234,509
Correct Answer
A. True
Explanation
All of the numbers given in the options are rational numbers. A rational number is any number that can be expressed as a fraction or a ratio of two integers. The first option, 1/6, is a fraction and can be written as the ratio of the integers 1 and 6. The second option, 0.425, can be written as the fraction 425/1000, which can be simplified to 17/40. The third option, 1, can be written as 1/1. The fourth option, 1,234,234,509, is an integer and can be written as the fraction 1,234,234,509/1. Therefore, all of the given numbers are rational numbers, making the statement "All of the following numbers are rational" true.
6.
The product of two rational numbers is always a rational number.
Correct Answer
B. True
Explanation
A rational number can be expressed as a fraction p/q, where p and q are integers, and q is not zero. When you multiply two fractions (p/q) * (r/s), the result is (pr) / (qs). Since the product of two integers is always an integer, the result is still a fraction with integers in the numerator and denominator, making it a rational number.
7.
Repeating decimals such as 0.2222222 are rational.
Correct Answer
A. True
Explanation
Repeating decimals can be expressed as a fraction, making them rational numbers. In this case, the repeating decimal 0.2222222 can be written as the fraction 2/9, which shows that it is indeed rational.
8.
Numbers that may be expressed as fractions are rational.
Correct Answer
A. True
Explanation
Numbers that may be expressed as fractions are rational because a rational number is defined as any number that can be expressed as a fraction, where the numerator and denominator are both integers. Fractions are written in the form of a/b, where a and b are integers and b is not equal to zero. Therefore, any number that can be written in this form is considered rational.
9.
Negative numbers may not be classified as rational numbers.
Correct Answer
B. False
Explanation
Negative numbers can be classified as rational numbers. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Negative numbers can be written as a fraction with a negative numerator and a positive denominator, making them rational. Therefore, the statement that negative numbers may not be classified as rational numbers is false.
10.
All positive numbers are rational.
Correct Answer
B. False
Explanation
The statement "All positive numbers are rational" is false. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. However, there are positive numbers that cannot be expressed in this form, such as the square root of 2 or pi. These numbers are called irrational numbers. Therefore, not all positive numbers are rational, making the statement false.