Question

how many rational numbers are there between 1 and 3​

Answer 1

Step-by-step explanation:

only one rational number is 2........

Answer 2

Given:

Two numbers 1 and 3.

To find:

The rational numbers present between 1 and 3.

Solution:

As we know that a number is said to be a rational number if it can be written in the p/q form.

So,

as given, we have,

Two rational numbers

$\frac{1}{1} \: and \: \frac{3}{1}$

Here, the denominators of both fractions are the same.

Now, if we want to find 'n' rational numbers between two numbers then we will multiply the n/2 in both numerator and denominator of two numbers.

So,

Now, we will find four rational numbers between 1 and 3. So,

$\frac{1 \times 2}{1 \times 2} \: and \: \frac{3 \times 2}{1 \times 2}$

$\frac{2}{2} \: and \: \frac{6}{2}$

Four rational numbers between 1 and 3 are-

3/2, 4/2, 5/2, 6/2

Similarly,

Now we will find the ten rational numbers between 1 and 3. So,

$\frac{1 \times 5}{1 \times 5} \: and \: \frac{3 \times 5}{1 \times 5}$

$\frac{5}{5} \: and \: \frac{15}{5}$

The ten rational numbers are-

6/5, 7/5...15/5

Hence, there are infinite rational numbers between 1 and 3.