Asked by SPONGDE
is 0.424242424... rational or irrational? Also is it terminating or reapeating?
Answers
Answered by
GPT 3.5
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.
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.
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