Choose the mixed number that is equivalent to this decimal. 3.242424…
The correct answer and explanation is:
To convert the repeating decimal 3.242424… to a mixed number, follow these steps:
Step 1: Write the decimal as a sum of its whole number and fractional parts.
The decimal 3.242424… can be broken into the whole number part, which is 3, and the repeating fractional part, which is 0.242424…
So, we have: 3.242424…=3+0.242424…3.242424… = 3 + 0.242424…
Step 2: Set up the repeating decimal as a fraction.
Let x=0.242424…x = 0.242424….
To eliminate the repeating decimal, multiply both sides of the equation by 100 (since the decimal repeats every two digits): 100x=24.242424…100x = 24.242424…
Now, subtract the original equation x=0.242424…x = 0.242424… from this new equation: 100x−x=24.242424…−0.242424…100x – x = 24.242424… – 0.242424… 99x=2499x = 24
Step 3: Solve for xx.
Now, solve for xx by dividing both sides of the equation by 99: x=2499x = \frac{24}{99}
Step 4: Simplify the fraction.
The greatest common divisor (GCD) of 24 and 99 is 3. So, divide both the numerator and the denominator by 3: x=24÷399÷3=833x = \frac{24 \div 3}{99 \div 3} = \frac{8}{33}
Step 5: Combine with the whole number.
The whole number part of the decimal was 3, so now add the fraction 833\frac{8}{33} to it: 3+833=38333 + \frac{8}{33} = 3 \frac{8}{33}
Final Answer:
The mixed number equivalent to the decimal 3.242424… is 38333 \frac{8}{33}.