Irrational Numbers

Multiplying 8 by any irrational number will produce an irrational number. For example, if you multiply 8 by the square root of 2 (approximately 1.414), the result, 8√2, is irrational. In general, the product of a rational number (like 8) and an irrational number is always irrational.

No, 7.73 is not an irrational number; it is a rational number. Rational numbers can be expressed as the quotient of two integers, and 7.73 can be written as 773/100. In contrast, irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

The quotient of a nonzero rational number and an irrational number is always an irrational number. This is because dividing a rational number (which can be expressed as a fraction of integers) by an irrational number cannot result in a fraction that can be simplified to a rational form. Therefore, the result remains outside the realm of rational numbers.

The fraction ( \frac{5}{3} ) is rational because it can be expressed as the ratio of two integers, where the numerator is 5 and the denominator is 3. Rational numbers are defined as numbers that can be written in the form ( \frac{a}{b} ) where ( a ) and ( b ) are integers and ( b ) is not zero. Since both 5 and 3 are integers and 3 is not zero, ( \frac{5}{3} ) is a rational number.

Negative 1.125 is a rational number because it can be expressed as a fraction. Specifically, it can be written as -9/8, which consists of an integer numerator and a non-zero integer denominator. Therefore, since it can be represented in this form, it is classified as rational.

3.14159 is an irrational number because it cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal, which is characteristic of irrational numbers. In fact, 3.14159 is a rounded approximation of the mathematical constant π (pi), which is also irrational.

0.1875 is a rational number because it can be expressed as a fraction. Specifically, it can be written as 1875/10000, which simplifies to 3/16. Rational numbers are defined as numbers that can be represented as the quotient of two integers, and since 0.1875 meets this criterion, it is considered rational.

No, 0.3754152 is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and since 0.3754152 can be represented as 3754152/10000000, it qualifies as rational. Irrational numbers, on the other hand, cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

No, -2.3 is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and -2.3 can be written as -23/10. In contrast, irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

15 divided by 4 is a rational number. When you divide 15 by 4, you get 3.75, which can be expressed as a fraction (15/4). Since rational numbers are defined as numbers that can be expressed as the quotient of two integers, 15 divided by 4 fits this definition.

rational because it has ended

The number 7.11 is a rational number because it can be expressed as a fraction, specifically ( \frac{711}{100} ). Rational numbers are defined as numbers that can be represented as the quotient of two integers, and since 7.11 meets this criterion, it is classified as rational.

1.7 is a rational number because it can be expressed as a fraction, specifically ( \frac{17}{10} ). Rational numbers are defined as numbers that can be written as the quotient of two integers, where the denominator is not zero. Since 1.7 meets this criterion, it is classified as rational.

No, 5.3 is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and 5.3 can be written as 53/10. Therefore, since it can be represented as a fraction, it is classified as rational.

No, all real numbers are classified as either rational or irrational. Rational numbers can be expressed as the quotient of two integers, while irrational numbers cannot be expressed as such and have non-repeating, non-terminating decimal expansions. Thus, there are no real numbers that fall outside these two categories.

No, 3.142857 is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and 3.142857 can be represented as 22/7, which indicates that it is a rational number. Irrational numbers, on the other hand, cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

0.09 is a rational number because it can be expressed as a fraction, specifically 9/100. Rational numbers are defined as numbers that can be written as the quotient of two integers, and since 0.09 fits this definition, it is classified as rational.

Yes, 5.56776436283 is an irrational number. An irrational number cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion. Since the decimal representation provided appears to be a non-repeating decimal, it indicates that the number is irrational.

No, 8.9745 is not an irrational number; it is a rational number because it can be expressed as a fraction. Specifically, it can be written as 89745/10000, which is the ratio of two integers. Rational numbers are those that can be represented as the quotient of two integers, and 8.9745 fits that definition.

The number 1.4141414141 is a rational number because it can be expressed as a fraction of two integers. Specifically, it can be represented as 141414141/100000000, which is a finite decimal. In contrast, the square root of 2, which is approximately 1.41421356..., is an example of an irrational number.

The number 2.343443444 is a rational number because it can be expressed as a fraction. Specifically, it can be written as ( \frac{2343443444}{1000000000} ). Since it has a finite decimal representation, it qualifies as rational.

sqrt(16) = +/- 3

Both +4 & -4 are rational.

NB The square roots of prime numbers are irrational

e.g. sqrt(2) = 1.413213562....

sqrt(3) = 1.732050808....

sqrt(5) = 2.236067978....

et seq.,

Oh honey, 1.67 is as rational as a well-organized sock drawer. It's a decimal number that can be expressed as a fraction, so it falls into the rational number club. No need to overcomplicate things, darling.

Oh, dude, negative square roots are actually considered irrational numbers. I know, right? It's like, they're not rational because they can't be expressed as a simple fraction. So yeah, negative square roots are definitely in the irrational club. Cool, right?

7 over 8, which can be written as 7/8, is a rational number. 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. Since 7 and 8 are both integers, and 8 is not zero, 7/8 is a rational number.