Find a rational number and an irrational number that are between 6.2 and 6.5. include the decimal approximation of the irrational number to the nearest hundredth.

We need to find a rational number and an irrational between 6.2 and 6.5.

Please see, we need to check the 10th place values of given numbers 6.2 and 6.5.

10th place value of 6.2 is 2 and tenth place value of 6.5 is 5.

So, we need to find a rational number and an irrational that has 10th place value between 2 and 5.

So, we could take 10th place value for a rational number and an irrational as 3 and 4.

Let us understand what a rational number and what and an irrational is.

A rational is the number (decimal number or any other number) that can be written on a fraction form. For example 2/5, 2/3 etc.

So, a rational number between 6.2 and 6.5 is 6.3.

An irrational number is a number (decimal number or any other number) that can't be written in the from of a fraction. For example 1.334454623, sqrt(2) etc.

So, an irrational number between 6.2 and 6.5 is 6.4231253465.

Let us round 6.4231253465 to nearest hundredth ( three decimal places).

6.4231253465  ≈ 6.423

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: