Types of Numbers - Algebra 2

The whole numbers are defined to be 0 and the so-called counting numbers, or natural numbers 1, 2, 3, and so forth. Negative integers and are not included in this set.

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set - - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.

The whole numbers are defined to be 0 and the so-called counting numbers, or natural numbers 1, 2, 3, and so forth. Negative integers and are not included in this set.

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set - - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Every element in the set is equal to raised to an even-numbered power, so when each exponent is divided by 4, the remainder will be either 0 or 2. Therefore, each element is equal to either 1 or . Consequently, the set includes no imaginary numbers.

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Every element in the set is equal to raised to an even-numbered power, so when each exponent is divided by 4, the remainder will be either 0 or 2. Therefore, each element is equal to either 1 or . Consequently, the set includes no imaginary numbers.

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set - - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.

By the Quotient of Powers Property,

.

Therefore, each element, the square root of a fraction, can be seen to be the fraction of the square roots of the individual parts. Each numerator and denominator is a perfect square, so each square root is a fraction of integers:

By definition, any integer fraction, being a quotient of integers, is a rational number, so all elements in the set are rational.

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Every element in the set is equal to raised to an even-numbered power, so when each exponent is divided by 4, the remainder will be either 0 or 2. Therefore, each element is equal to either 1 or . Consequently, the set includes no imaginary numbers.

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set - - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.

By the Quotient of Powers Property,

.

Therefore, each element, the square root of a fraction, can be seen to be the fraction of the square roots of the individual parts. Each numerator and denominator is a perfect square, so each square root is a fraction of integers:

By definition, any integer fraction, being a quotient of integers, is a rational number, so all elements in the set are rational.

By the Quotient of Powers Property,

.

Therefore, each element, the square root of a fraction, can be seen to be the fraction of the square roots of the individual parts. Each numerator and denominator is a perfect square, so each square root is a fraction of integers:

By definition, any integer fraction, being a quotient of integers, is a rational number, so all elements in the set are rational.

The whole numbers are defined to be 0 and the so-called counting numbers, or natural numbers 1, 2, 3, and so forth. Negative integers and are not included in this set.

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Every element in the set is equal to raised to an even-numbered power, so when each exponent is divided by 4, the remainder will be either 0 or 2. Therefore, each element is equal to either 1 or . Consequently, the set includes no imaginary numbers.

By the Quotient of Powers Property,

.

Therefore, each element, the square root of a fraction, can be seen to be the fraction of the square roots of the individual parts. Each numerator and denominator is a perfect square, so each square root is a fraction of integers:

By definition, any integer fraction, being a quotient of integers, is a rational number, so all elements in the set are rational.

For a number to be prime it must only have factors of one and itself.

10 has factors 1, 2, 5, 10.

15 has factors 1, 3, 5, 15.

18 has factors 1, 2, 3, 6, 9, 18.

The only factors of 13 are 1 and 13. As such it is prime.

Multiplying out using FOIL (First, Inner, Outer, Last) results in,

.

Remember that

is a real number, because you can represent it on the Cartesian coordinate plane, but it is irrational because it cannot be represented by a fraction of two integers. Natural numbers are integers greater than 0.

Natural numbers are simply whole, non-negative numbers.

Using this definition, we see only one set of numbers within our answer choices containing only whole, non-negative numbers. Any set containing decimals or negative numbers, will violate our defintion of natural numbers and thus be an incorrect answer.