Find five rational numbers between 1 and 2
Numbers or numerals are used in our daily life for counting objects, date, time, money which cannot be counted without numbers. The numbers are used for measurements and labeling. In mathematics, various types of numbers are involved such as odd numbers, even numbers, rational or irrational numbers, etc. These numbers allow to carry out various arithmetic operations such as summation, subtraction, multiplication, division, exponential, etc.
Numbers are the standard figures used for measurement of quantities, labeling, and carrying out various calculations. Numbers are written in symbols such as ‘2’.
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The 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 system to express numbers in various forms. It is the unique way of representation in which numbers are represented in arithmetic and algebraic structure.
The value of a number is determined by the digit, its place value in the number, and the base of the number system under the preferred category 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 numbers that count from 1 to infinity. 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 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 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?
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, 2/10 is a rational number that expresses that integer 2 is divided by integer 10.
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 3.16534…….
Now, let’s look into the question
What are the five rational numbers between 1 and 2?
The five rational numbers between 1 and 2 are 11/10, 12/10, 13/10, 14/10 and 15/10.
To find out a set of rational numbers between two numbers suppose p and q we need to express numbers p and q in rational form.
Lets express 1 and 2 as rational numbers as
=>1 = 1×10/10 = 10/10
=>2 = 2×10/10 = 20/10
Hence, the five rational numbers between 1 and 2 are 11/10, 12/10, 13/10, 14/10 and 15/10.
Question 1: What are the five rational numbers between 0 and 1?
The rational numbers between 0 and 1 are 15, 24, 34, 41, and 55.
Question 2: How can we express rational numbers?
We can express a rational number as p/q, where, q is a non-zero denominator.
Question 3: What are the rational numbers between 3 and 4?
The rational numbers between 3 and 4 are 31/10, 32/10, 33/10, 34/10, 35/10, 36/10, 37/10, 38/10, and 39/10.