Question

is 0.424242424... rational or irrational? Also is it terminating or reapeating?

Answer 1

The number 0.424242424... is rational and repeating.

To see why, we can represent it as a fraction by using the method of "repeating decimals." Let's denote x = 0.424242424... and multiply it by 100 to eliminate the infinite repeating part:

100x = 42.42424242...

Next, subtract x from both sides:

100x - x = 42.42424242... - 0.42424242...

This simplifies to:

99x = 42

Dividing both sides by 99, we get:

x = 42/99 = 14/33

Therefore, 0.424242424... is rational and can be expressed as the fraction 14/33.