Answer and Explanation: **The decimal 2.5 is a rational number**.

That is, the decimals either do not exist, as in 5, (which is 5/1). Or the decimals terminate, as in 2.4, (which is 24/10). Or the decimals repeat with a pattern, as in 2.333..., (which is 7/3). This way of defining a rational number, however, really misses the point.

Real numbers (R), (also called measuring numbers or measurement numbers). This includes all numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or 2.142857. It also includes all the irrational numbers such as π, √2 etc.

Since, 2.5 being the decimal number, it is not considered to be a whole number. However, it can be converted to a whole number by rounding it off to the nearest whole number. 2.5 rounded off to the nearest whole number is 3. Hence, the whole number of 2.5 will be 3.

The decimal 2.5 is a rational number. All decimals can be converted to fractions. The decimal 2.5 is equal to the fraction 25/10.

Solved Examples

Example 3: From the given series of numbers, find natural numbers. 41, (0.4), 5, 90, -91, 0, -7. Sol: Natural Numbers = 41, 5, 90.

Students are usually introduced to the number pi as having an approximate value of 3.14 or 3.14159. Though it is an irrational number, some people use rational expressions, such as 22/7 or 333/106, to estimate pi.

What are Non Real Numbers? Complex numbers, like √-1, are not real numbers. In other words, the numbers that are neither rational nor irrational, are non-real numbers.

Therefore, all of these rational and irrational numbers, including fractions, are considered real numbers. Real numbers that include decimal points are known as floating point numbers because the decimal floats within the numbers. Integers or whole numbers cannot be floating point numbers.

3.14 can be written as a fraction of two integers: 314100 and is therefore rational.

Answer and Explanation: The decimal 0.25 is a rational number.

These are the set of all counting numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, ……. ∞. Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

The whole numbers are set of real numbers that includes zero and all positive counting numbers. Whereas, excludes fractions, negative integers, fractions, and decimals. Since, 3.2 being the decimal number, it is not considered to be a whole number.

Examples: 3+6i (3 is the real part, 6i is the imaginary part)

The number 5 is present in the real numbers. Therefore, the number 5 is a rational, whole, integer and real number.

real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting.

The numbers 3.5, −0.003, 2/3, π, and √2 are all real numbers. The real numbers include the rational numbers, which are those which can be expressed as the ratio of two integers, and the irrational numbers, which cannot.

1.25 is a rational number. A rational number is any number that can be written as a fraction.

Definition of a Rational Number

For example, 0.5 is a rational number. It is not a whole number, natural number, or integer, but it can be expressed as 1/2, which a fraction of two other integers: 1 is the numerator and 2 is the denominator. So, 0.5, or 1/2, is a rational number.

The decimal 0.7 is a rational number. It is read as seven tenths and is equivalent to the fraction 7/10.

2/3 is a rational number as it can be expressed in the form of p/q where p, q are integers and q is not equal to zero.

Explanation: Natural numbers are 1,2,3,4,.. i.e. only positive non-zero whole numbers. Whole numbers also include 0 along with natural numbers and hence −4 is neither a natural number nor a whole number.