Numerals are the mathematical figures used in financial, professional as well as a social field in the social world. The digits and place value in the number and the base of the number system determine the value of a number. Numbers are used in various mathematical operations as summation, subtraction, multiplication, division, percentage, etc. which are used in our daily businesses and trading activities.
What are numbers?
Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc. which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system.
Numbers generally also known as numerals are the mathematical values used for, counting, measurements, labeling and measuring fundamental quantities.
Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2,4,7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
Types Of Numbers
There are different types of numbers categorized into sets by the number system. The types are described below:
- Natural numbers: Natural numbers are the positive counting numbers that count from 1 to infinity. The subset doesn’t include fractional or decimal values. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N=1,2,3,4,5,6,7,……………
- Whole numbers: Whole numbers are positive natural numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W’. The set can be represented as W=0,1,2,3,4,5,………………
- Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z‘. The set of integers can be represented as Z=………..,-5.-4,-3,-2,-1,0,1,2,3,4,5,………….
- Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can also be expressed in the fractional form in some cases. It can be expressed as 2.5,0.567, etc.
- Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R‘.
- Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
- Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
- Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.
What are Rational Numbers?
Rational numbers are of the form p/q, where p and q are integers and q ≠ 0. Because of the underlying structure of numbers, p/q form, most individuals find it difficult to distinguish between fractions and rational numbers. When a rational number is divided, the output is in decimal form, which can be either ending or repeating. 3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1.
Examples of Rational Numbers
3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1. The number “0” is also rational since it may be represented in a variety of ways, including 0/1, 0/2, 0/3, and so on.
Is 1.5/7.5 a rational number?
Answer:
Yes, 1.5/7.5 is a Rational Number. As rational numbers can be expressed as decimals values as well as fractions. The number can also be simplified to 1/5 which is the ratio of two integers.
Take a look at the below proof:
Proof:
The number 1.5/7.5 can be represented as shown below:
=> 1.5/7.5 = 15/75
This can be further broken down as,
⇒ 15/75 = 1/5
The number 1/5 is the ratio of two integers that are 1 integer divided by 5 integer and expressed in fraction form (as p/q where q is not equal to 0).
Similar Questions
Question 1: Is √7 a rational number or an irrational number?
Answer:
A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √5 cannot be expressed in the form of p/q. Alternatively, 7 is a prime number. This means that the number 7 has no pair and is not divisible by 2. Hence, √7 is an irrational number.
Question 2. What is 25/10 as a whole number?
Answer:
Given:- The number is 25/10
Explanation:
The whole numbers are numbers that start from zero.
Consider the number 25/10 as Y.
Y = 25/10
Dividing 25/10 to get the whole number,
so we get,
Y = 25/10
Y = 2.5
Rounding it off to the nearest whole number, we get 3. Yes, decimal values can be rational numbers as rational numbers can be written in both fraction as well as decimal form. But, the decimal value needs to be definite or have repeating digits after decimal point.
Question 3: Is √16 a rational number or an irrational number?
Answer:
A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √16 can be expressed in the form of p/q as it is equal to 4. Alternatively, 4 is not a prime number. This means that the number 4 is divisible by 2. Hence, √16 is a rational number.