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Is 3.5 a rational or irrational number?

  • Last Updated : 05 Aug, 2021

Number system includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures as well as words accordingly. For example, the numbers like 40 and 65 expressed in the form of figures can also be written as forty and sixty-five.

A Number system or numeral system is defined as a standardized system to express numbers. It is the unique way of representation in which numbers are represented in arithmetic and algebraic structure.

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Definition of Numbers

Numbers are the mathematical or arithmetic figures used for the purpose of counting, measuring, and other arithmetic calculations. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.

Numbers are used in various arithmetic operations as addition, subtraction, multiplication, etc which are applicable in daily businesses and trading activities. Numerals or numbers are the mathematical values used for, counting, measurements, labeling or recognizing time, and for many other activities. Numbers are generally also known as numerals.

The value of a number is determined by:

  • The digit
  • Its place value in the number
  • The base of the number system

Types Of Numbers

There are different types of numbers categorized into sets by the number system. The types are described below:

  • Natural numbers: The positive counting numbers that count from 1 to infinity are natural numbers. 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: The positive counting numbers including zero, which counts from 0 to infinity are whole numbers. 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: 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 are integers. 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 considered as a fraction of numbers with denominator 10 or any power of 10. It can be expressed as 2.5,0.567, etc.
  • Real number: The set of numbers that include all the positive integers, negative integers, fractions, and decimal values, whereas,  excludes any imaginary number is called real number. It is generally denoted by ‘R”.
  • Complex number: The set of numbers that include imaginary numbers are complex numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
  • Rational numbers: The numbers that can be expressed as the ratio of two integers are rational numbers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
  • Irrational numbers: The numbers that cannot be expressed in fractions or ratios of integers are irrational numbers. 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?

The numbers which can be expressed as fractions or ratio of two integers and also can be written as a positive number, negative number, prime, and even zero is called rational numbers.

It can be expressed as p/q, where q ≠0

For example, 2/3 is a rational number that expresses that integer 2 is divided by integer 3.

What are 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.



For example 2.65432……..

Is 3.5 a Rational or Irrational Number?

Answer:

Number 3.5 is a rational number. Since rational numbers can also be expressed as decimals with repeating digits after the decimal point.

Take a look at the proof given below:

Proof:

The given number 3.5 can be expressed as

=>3.5=35/10

This can be further broken down as

=>35/10=7/2

The number7/2 is the ratio of two integers that are 7 integers divided by 2 integers and expressed in fraction (as p/q where q is not equal to 0).

Similar Questions

Question 1: What are the five rational numbers between 0 and 1?

Answer:

The rational numbers between 0 and 1 are 12,21, 34, 41, and 51.

Question 2: How can we express rational numbers?

Answer:

We can express a rational number as p/q, where, q is a non-zero denominator.

Question 3: Is 0 a rational number?

Answer:

Yes, 0 is a rational number as it can be expressesd in p/q form as 0/1 . Here, the denominator is a non-zero value which means 0 is a rational number.

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