Question
Asked By MysticSkyline31 at
Answered By Expert
Rex
Expert · 5.4k answers · 5k people helped
Solution By Steps
Step 1: Identify the given number
Given number is
0.4.
Step 2: Determine if the sum is rational or irrational
To produce an irrational number, the number added to
0.4 must be irrational. If the sum is rational, the added number is rational; if the sum is irrational, the added number is irrational.
Step 3: Add each option to 0.4 and check if the sum is rational or irrational
Adding
\frac{2}{7} to
0.4 results in a rational number.
Adding
\sqrt{9} to
0.4 gives
3.4, a rational number.
Adding
0.444\ldots to
0.4 results in
0.844\ldots, a rational number.
Adding
3\pi to
0.4 gives
0.4 + 3\pi, which is irrational since
\pi is irrational.
Final Answer
The number that produces an irrational sum when added to
0.4 is
3\pi (Option D).
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