How Many Fractions Lie Between 0 and 1

Introduction

The answer is infinite. Fractions are defined as the parts of a whole. The whole can be an object or a group of objects. The fraction has also termed a portion or section of any quantity. It is denoted by using ‘/’ symbols, such as a/b. For example, 1/2 is a fraction where the upper part denotes the numerator and the lower part is the denominator.

Fractions Lie Between 0 And 1

These can be answered in the following ways:

Infinite:

0...1/10...2/10...3/10......9/10...1

Between 0 and 110 there are:

0...1/100...2/100......9/100...1/10

And from 0 to 1, this goes all the way to 99/100...1

Then between 0 and 1/100, we have the same idea, endlessly repeating until we have:

\begin{aligned}

&0...\frac{1}{\infty}...\frac{2}{\infty}...\frac{3}{\infty}...

\end{aligned}

If you are asking how many different fractions lie in this range the answer is an infinite amount. If you are asking what fraction lies in the centre it is ½.

The members A = {(0,1/n)U(1/n,n/n+1): n€N, the set of all natural numbers} are countably infinite. An infinite number of fractions are there.

How Many Fractions Are Between 0 And 1?

There would be infinite fractions between 0 and 1 as there are infinite numbers between 0 and 1.

Take the example of 0.01 a number between 0 and 1.

Even that can be represented by a fraction of 1/100.

Say several 0.85.

It can be represented by 85/100.

Take any decimal number between 0 and 1 and it can be represented as a fraction.

Now think and tell how many decimal numbers are between 0 and 1.

if you thought it was infinite then you are right.

As there are infinite decimal numbers, we can represent each decimal with a fraction.

Hence there would be infinite fractions between 0 and 1.

There are infinite fractions between any two real numbers.

This is because the difference between any two numbers can be divided by an infinite no. of numbers.

On the number line, this can be visualized as dividing a line segment whose length is equal to the difference between the two given numbers.

The line segment can be divided into infinite no. of smaller line segments.

Therefore we have an infinite no. of numbers between any two numbers (each smaller line segment giving a number whose difference from one of the given numbers is equal to the length of the line segment).

And, if the two given numbers are integers like 1 and 0, the infinite no. of numbers consists only of fraction and irrational numbers.

Conclusion

There would be infinite fractions between 0 and 1 as there are infinite numbers between 0 and 1.

As there are infinite decimal numbers between 0 and 1 we can represent each decimal with a fraction.

Hence, there would be infinite fractions between 0 and 1.