Number Identification: Rational Or Irrational Quiz

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.

Pi (π) is an irrational number, meaning it cannot be expressed as a simple fraction or ratio of two integers. Its decimal representation is non-terminating and non-repeating, 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.

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.

An irrational number cannot be expressed as a simple fraction of two integers. The square root of 2 is a non-terminating, non-repeating decimal, meaning its decimal representation goes on forever without a pattern. This makes it impossible to write as a fraction, thus making it irrational.

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 non-repeating, non-terminating decimal expansion.

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.

An irrational number is a number that cannot be expressed as a fraction of two integers. Irrational numbers have decimal representations that neither terminate nor repeat. The number 9.946787839395329 is an irrational number because its decimal representation does not terminate or repeat. The other numbers are rational because they can be expressed as fractions: -3 = -3/1, 4 = 4/1, and -22 = -22/1.

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. 

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.

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.