How Many Rational Numbers Between Two Rational Numbers?

There are an infinite number of rational numbers in between two rational numbers.

The word "ratio" is where the term "rational" first appeared. Rational numbers are, therefore, closely tied to the idea of fractions, which stand for ratios. In other words, a reasonable number can be represented as an integer-based fraction with an integer numerator and denominator.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter Q stands for the set of rational numbers.

How To Check A Number Is A Rational Number

Check out the conditions below to determine whether a number is rational.

• It is shown as the ratio p/q, where q equals zero.

• It is possible to represent the ratio p/q in decimal form, which is a further simplification.

Rational number sequence:

• the number zero, as well as positive and negative numbers

• can be written as a fraction

List Of Rational Numbers

There are an unlimited amount of rational numbers, as can be shown from the facts above. As a result, it is impossible to compile a complete list of rational numbers. A few examples of rational numbers are 9, 4.57, 3/4, 0, -7, and so forth. This demonstrates that all decimals (including terminating decimals and recurring decimal numbers), whole numbers, integers, fractions, and decimals are thought to be rational numbers.

Where Q is a Rational number, Z is an integer, W is a Whole Number, N is a Natural number

Rational Numbers Between Two Rational Numbers

Between any two rational integers, there is an endless number of possible inserts. Dense Property is the name given to this property of rational numbers.

To find them we have 2 cases:-

• Rational numbers with the same denominators

• Checking the denominator value is the first and most very important in determining the rational numbers that lie between two rational numbers.

• Verify the numerator value in the event that the denominators are the same.

• In this case, simply write the fractions by adding 1 to the numerator. if the numerators differ by a significant amount while maintaining the original denominator value.

• you can also multiply the numerators and denominators by 10. if the numerators differ by a value less than a number of rational numbers to be discovered.

• Rational numbers with different denominators

• The denominators must first be equalised in order to find rational numbers that lie between two rational numbers with different denominators.

• By calculating their LCM or by multiplying the denominators of one by the numerator and the denominator of another, you can equilibrate the denominators.

Examples

• The rational number between 1/2 , and 7/2 are

2/2 , 3/2, 4/2, 30/20, 40/20…………… etc.

• The rational number between 1/2 and 3/4 are

4/8, 6/8 40/80, 60/80 ……………. etc.