Question

Choose the mixed number that is equivalent to this decimal.

3.242424…
3833

31225

314

315

Answer 1

To convert the decimal \( 3.242424... \) into a mixed number, we can first separate the whole number part from the decimal part.

The whole number part is \( 3 \).

Next, we focus on the decimal part \( 0.242424... \). This decimal is repeating, and we can express it as a fraction. We can let \( x = 0.242424... \).

To eliminate the repeating part, we can multiply \( x \) by 100:

\[
100x = 24.242424...
\]

Now, we can set up the equation by subtracting the original \( x \) from this new equation:

\[
100x - x = 24.242424... - 0.242424...
\]

This simplifies to:

\[
99x = 24
\]

Now, we can solve for \( x \):

\[
x = \frac{24}{99}
\]

Next, we can simplify the fraction \( \frac{24}{99} \). The greatest common divisor (GCD) of 24 and 99 is 3, so we divide both the numerator and the denominator by 3:

\[
x = \frac{24 \div 3}{99 \div 3} = \frac{8}{33}
\]

Now we can express the entire number. Combining the whole part and the fractional part gives us:

\[
3 + \frac{8}{33} = \frac{3 \cdot 33 + 8}{33} = \frac{99 + 8}{33} = \frac{107}{33}
\]

To write it as a mixed number, we can see that \( 3 + \frac{8}{33} \) is indeed already a mixed number.

So the mixed number equivalent to \( 3.242424... \) is \( 3 \frac{8}{33} \).

Now, looking at the answer choices:

- \( 3833 \)
- \( 31225 \)
- \( 314 \)
- \( 315 \)

None of these seem to correspond directly. The closest answer appears to be \( 3 \frac{1}{4} \) (which is not an available option).

Thus, the equivalent mixed number to \( 3.242424... \) in common representation is not directly in the list, as it would need \( \frac{8}{33} \) represented.

If we needed to see if \( 3.24 \) might round to anything, \( 314 \) could be an approximation (but incorrect with \( 3 \frac{8}{33} \)), and \( 3.25 \) is closer to \( \frac{1}{4} \).

The answer you are looking for remains not explicitly listed but assuredly \( \frac{107}{33} \) or \( 3 \frac{8}{33} \) if asked for a conversion against choices.

So, your answer is that none of the given options accurately conveys \( 3.242424... \), but \textbf{it can be expressed as a mixed number in other forms however it will not directly match what's here}.