Is 2.6 a rational number?
Numerals or numbers are the mathematical figures often applicable to conduct operations like calculations, counting, measurements, or recognizing time and for many other activities. Numerals are generally called numbers. The numerals are used in various arithmetic operations as addition, subtraction, multiplication, etc which are applicable in daily businesses and trading activities.
Numbers can be expressed in the form of figures as well as words accordingly. For example, The numbers like 45, 63, and 1000 expressed in the form of figures can also be written as Forty-five, Sixty-three, and One thousand respectively. Mathematics includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc.
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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.
The Number system is a standardized system for the representation of numbers, which includes categories like, zero, negative numbers, rational numbers, irrational numbers, and complex numbers. In addition to that, it also represents binary and decimal numbers. It provides a structure to the arithmetic and algebraic mathematical operations like addition, subtraction, multiplications, and divisions, etc.
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: Natural numbers are the positive counting numbers that count from 1 to infinity. The set of natural numbers is denoted 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 counting numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is denoted 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 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’.
A Rational number is defined as a real number in the form of A/B where B is not equal to zero. In simple words, we can state that any fraction with a non-zero denominator is a rational number.
Rational numbers involve all positive integers, negative integers. Even 0 is rational as it has a non-zero denominator.
The mathematical representation of the rational numbers is as A/B
B is not equal to Zero(0)
Some Examples of Rational Numbers
Rational numbers are fractional or decimal values. Some of the examples of rational numbers are
- 2/5 is a rational number that is a ratio of two integers 2 and 5.
- 0.5 is a rational number that can also be written as 1/2 which is the ratio of two integers 1 and 2.
Now let’s jump into the question.
Is 2.6 a rational number?
Yes 2.6 is a Rational Number. As rational numbers can be expressed as decimals values as well as fractions. The number can also be written as 26/10 which is the ratio of two integers.
Take a look at the below proof.
The number 2.6 can be represented as shown below:
=> 2.6 = 26/10
This can be further broken down as,
⇒26/100 = 13/5
The number 13/5 is the ratio of two integers that are 13 integers divided by 5 integers and expressed in fraction form (as p/q where q is not equal to 0).
Question 1: Is 2.5 a rational number?
Yes, 2.5 is a rational number as its fractional expression will be 5/2 which is a ratio of two integers thatis 5 integer being divided by 2 integer.
Question 2: Can decimal values be rational numbers?
Yes, decimal values can be rational numbers as rational numbers canbe written in both fraction as well as decimal form. But, the decimalvalue needs to be definite or have repeating digits after decimal point.