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Question

Question
Which number produces an irrational number when added to 0.4 ? A. $\frac{2}{7}$ B. $\sqrt{9}$ C. $0.444 \ldots$ D. $3 \pi$

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Rex

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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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