Find rational numbers between 3.5 and 4.5

• Last Updated : 17 Aug, 2021

Numbers have been a big part of our daily life in the financial, social, and professional sectors, whether it be buying commodities, making payments, sales, or even while communicating. No matter which method or number system we prefer they are essential figures for measuring, identifying, calculating, etc.

The numerals are used in various arithmetic operations as addition, subtraction, multiplication, etc which are applicable in daily businesses and trading sectors. Numbers can be expressed in both figures and words. The number system is a constituent of various types of numbers that are real numbers, complex numbers, even numbers, rational numbers, whole numbers, etc.

Numbers are the arithmetic figures used for the purpose of making arithmetic calculations. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.

The number system is used for measuring fundamental quantities, determine the distance, displacement, time, and many other physical values.

The Number system is a standardized method for the representation of numbers, which includes categories like, zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

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 or all whole numbers except 0 that count from 1 to infinity. The symbol of a set of natural numbers is  ‘N’. It is the number 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 or all-natural numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The symbol of a 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 natural numbers, zero as well as all negative natural numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The symbol of a set of integers is d ‘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 is a fraction of two numbers with denominator 10 or any positive power of 10 or consists of a decimal point is a decimal number. It can be expressed as 2.5,0.567, etc.
• The 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. The symbol of the real number is  ‘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?

A Rational number can be defined as a real number in the form of the fraction that is of p/q where q 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 p/q

Where,

q is not equal to Zero(0)=>7/2 = 7/2 × 2/2 = 14/4

Now, let’s jump into the question,

Find rational numbers between 3.5 and 4.5

The rational numbers between 3.5 and 4.5 will be 36/10, 37/10, 38/10, 39/10, 40/10, 41/10, 42/10, 43/10, and 44/10.

To find out a set of rational numbers between two numbers let’s suppose p and q, we need to express the numbers in the form of a ratio.

Here, the two numbers are 3.5 and 4.5

Proof:

Let’s express the numbers 3.5 and 4.5 as rational numbers or in ratio.

=>3.5 = 35/10

=>4.5 = 45/10

Hence, the rational numbers between 35/10 and 45/10 are  36/10, 37/10, 38/10, 39/10, 40/10, 41/10, 42/10, 43/10, and 44/10.

Similar Questions

Question 1: What are the five rational numbers between 3/5 and 4/5?

The five rational numbers between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22/30, and 23/30.

To find out a set of rational numbers between two numbers suppose A and B we need to express numbers A and B in rational numbers.

Proof:

Let’s multiple both the numbers with 6/6 to make denominators equal.

=>3/5 = 3/5 × 6/6 = 18/30

=>4/5 = 4/5 × 6/6 = 24/30

Hence, the five rational numbers between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22/30, and 23/30.

Question 2: What are the rational numbers between 3/4 and 9/10?

The rational numbers between 3/4 and 9/10 are 16/20 and 17/20.

To find out a set of rational numbers two numbers A and B we need to express numbers A and B in rational numbers.

Proof:

Let’s multiply 3/4 by 5/5 and 9/10 by 2/2 to make the denominators equal.

=>3/4 × 5/5 = 15/20

=>9/10 × 2/2 = 18/20

Hence, the rational numbers between 3/4 and 9/10 are 16/20 and 17/20.

Question 3: What are the five rational numbers between 3/5 and 6/5?

The five rational numbers between 3/5 and 6/5 are 16/25, 17/25, 18/25, 19/25, and 20/25.

To find out a set of rational numbers two numbers A and B we need to express numbers A and B in rational numbers.

Proof:

Let’s multiply both the numbers with 5/5

=>3/5 × 5/5 = 15/25

=>6/5 × 5/5 = 30/25

Hence, the five rational numbers between 3/5 and 6/5 are 16/25, 17/25, 18/25, 19/25, and 20/25.

Question 4: What are the rational numbers between 2/5 and 3/4?

The rational numbers between 2/5 and 3/4 are 9/20, 10/20, 11/20, 12/20, 13/20, and 14/20.

To find out a set of rational numbers two numbers A and B we need to express numbers A and B in rational numbers.

Proof:

Let’s multiply 2/5 by 4/4 and 3/4 by 5/5 to make the denominators equal.

=>2/5 = 2/5 × 4/4 = 8/20

=>3/4 = 3/4 × 5/5 = 15/20

Hence, the rational numbers between 2/5 and 3/4 are 9/20, 10/20, 11/20, 12/20, 13/20, and 14/20.

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