The Correct Answer and Explanation is:
The correct answer is 3.8̅, which represents the repeating decimal 3.888…
To convert the mixed number 3 8/9 into a decimal, we can follow a two-step process. A mixed number consists of a whole number part and a fractional part. In this case, the whole number is 3, and the fraction is 8/9.
First, we focus on the whole number, which is 3. This number will form the part of our decimal that is to the left of the decimal point. So, we already know our final answer will be 3 followed by some decimal value.
Second, we need to convert the fractional part, 8/9, into a decimal. The way to convert any fraction to a decimal is to divide the numerator (the top number) by the denominator (the bottom number). Here, we must divide 8 by 9.
When you perform this division (8 ÷ 9), you will notice a pattern. Since 9 is larger than 8, the result will be less than 1.
- We start by dividing 8.0 by 9. 9 goes into 80 eight times (9 × 8 = 72).
- Subtracting 72 from 80 leaves a remainder of 8.
- We bring down another zero to make it 80 again. Once more, 9 goes into 80 eight times, leaving another remainder of 8.
This process will continue indefinitely, with the digit 8 repeating forever. This is known as a repeating decimal. We can write this as 0.888… To show that the 8 repeats, we use a bar notation (a vinculum) over the repeating digit: 0.8̅.
Finally, we combine the whole number part and the decimal part. We add the whole number 3 to the decimal we just found, 0.8̅.
3 + 0.8̅ = 3.8̅
Therefore, the mixed number 3 8/9 written as a decimal is 3.8̅, or 3.888…
