Find nine rational numbers between 0 and 1

• Difficulty Level : Hard
• Last Updated : 09 Aug, 2021

A rational number is a type of real number of the form p/q where q is not equal to zero in mathematics. Any fraction can be classified as a rational number if the denominator and numerator are both integers and the denominator is not zero. A decimal number, which can be either a terminating or recurring decimal, is the result of dividing a rational number.

Examples of Rational Numbers

3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1. The number “0” is also rational since it may be represented in a variety of ways, including 0/1, 0/2, 0/3, and so on. However, 1/0, 2/0, 3/0, and so on are irrational because they give us unlimited values.

How to Find the Rational Numbers between Two Rational Numbers?

Between two rational numbers, there exist “n” numbers of rational numbers. Two alternative approaches can be used to find the rational numbers between two rational numbers. Let’s have a look at the two distinct approaches.

Approach 1:

Calculate the equivalent fractions of the given rational numbers and calculate the rational numbers in between them. Those figures should be the necessary reasonable figures.

Approach 2:

Calculate the mean of the two rational numbers supplied. The necessary rational number should be the mean value. Repeat the method with the old and newly obtained rational numbers to find more rational numbers.

Find nine rational numbers between 0 and 1

Solution:

Approach 1:

Let us follow the first approach to find out the rational numbers between 0 and 1. The required rational numbers can be in between these numbers. One can choose any number with terminating or recurring decimals.

Hence, the nine rational numbers between 0 and 1 are 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9.

Approach 2:

Let us follow the second approach to find out the rational numbers between 0 and 1.

The formula to calculate the mean is given as:

m = sum of the terms/number of the terms

Here, the given terms are 1 and 0, so the mean is:

m = (1 + 0)/2 = 1/2 = 0.5

Now, the mean of 0.5 and 1 is:

m = (0.5 + 1)/2 = 1.5/2 = 0.75

Now, the mean of 0.75 and 1 is:

m = (0.75 + 1) / 2 = 1.75 / 2 = 0.875

Now, the mean of 0.875 and 1 is:

m = (0.875 + 1) / 2 = 1.875 / 2 = 0.9375

Now, the mean of 0.9375 and 1 is:

m = (0.9375 + 1) / 2 = 1.9375 / 2 = 0.96875

Now, the mean of 0.5 and 0 is:

m = (0.5 + 0) / 2 = 0.5 / 2 = 0.25

Now, the mean of 0.25 and 0 is:

m = (0.25 + 0) / 2 = 0.25 / 2 = 0.125

Now, the mean of 0.125 and 0 is:

m = (0.125 + 0) / 2 = 0.125 / 2 = 0.0625

Now, the mean of 0.0625 and 0 is:

m = (0.0625 + 0) / 2 = 0.0625 / 2 = 0.03125

Hence, the nine rational numbers between 0 and 1 are 0.03125, 0.0625, 0.125, 0.25, 0.5, 0.75, 0.875, 0.9375, and 0.96875.

Similar Questions

Question 1: What are the three rational numbers between 1 and 5?

Solution:

Here, the given terms are 1 and 5, so the mean is:

m = (1 + 5) / 2 = 6 / 2 = 3

Now, the mean of 1 and 3 is:

m = (1 + 3) / 2 = 4 / 2 = 2

Now, the mean of 3 and 5 is:

m = (5 + 3) / 2 = 8 / 2 = 4

Hence, the three rational numbers between 1 and 5 are 2, 3, and 4.

Question 2: What are the two rational numbers between 7 and 11?

Solution:

Here, the given terms are 7 and 11, so the mean is:

m = (7 + 11) / 2 = 18 / 2 = 9

Now, the mean of 7 and 9 is:

m = (7 + 9) / 2 = 16 / 2 = 8

Hence, the two rational numbers between 7 and 11 are 8 and 9.

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