Write 11/6 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
The Correct Answer and Explanation is:
To convert ( \frac{11}{6} ) to a decimal, we divide 11 by 6.
- Start by dividing 11 by 6. The whole number part of the division is 1, because (6) goes into (11) one time.
- Subtract (6) (1 multiplied by 6) from (11), which leaves a remainder of (5).
- Bring down a zero to make it (50).
- Now, divide (50) by (6), which gives (8) (since (6 \times 8 = 48)).
- Subtract (48) from (50), leaving a remainder of (2).
- Bring down another zero, making it (20).
- Divide (20) by (6), which gives (3) (since (6 \times 3 = 18)).
- Subtract (18) from (20), leaving a remainder of (2) again.
Since we continue to get a remainder of (2) after each calculation, the sequence of digits (1.8333\ldots) continues indefinitely. In decimal notation, we write this as:
[
1.8\overline{3}
]
The bar over the (3) indicates that (3) repeats indefinitely.
Explanation
Fractions can be converted to decimals by performing division of the numerator by the denominator. Here, ( \frac{11}{6} ) is an improper fraction (the numerator is larger than the denominator), so the result will be greater than 1. Through division, we find that ( \frac{11}{6} = 1.8333\ldots ), with the decimal part repeating. This type of decimal is known as a repeating decimal because a certain digit (or group of digits) repeats indefinitely.
In cases where the remainder repeats during division, the decimal expansion will also repeat. We use a bar notation to indicate the repeating part, making it easier to identify that only the digit (3) is repeating. Therefore, the correct answer is:
[
1.8\overline{3}
]