To find a rational number between 0.3333... and 0.4444..., we can convert these decimal representations into fractions and find an appropriate fraction in between them.
0.3333... can be written as 1/3, while 0.4444... can be written as 4/9. Therefore, we have the fractions 1/3 and 4/9 representing 0.3333... and 0.4444... respectively.
To find a rational number between them, we can take the average of these two fractions:
(1/3 + 4/9) / 2 = (3/9 + 4/9) / 2 = 7/18
Hence, 7/18 is a rational number between 0.3333... and 0.4444...
Now, to find an irrational number between them, we can choose any irrational number within this range, such as the square root of 2 (approximately 1.414).
Hence, the square root of 2 is an irrational number between 0.3333... and 0.4444...
Find one rational number and one irrational number between 0.3333.... and 0.4444....
1 answer