write the following rational number in decimal form of 11 / 6
The Correct Answer and Explanation is:
To write the rational number 11/6 in decimal form, divide the numerator by the denominator:11÷6=1.8333…11 ÷ 6 = 1.8333\ldots11÷6=1.8333…
The decimal form of 11/6 is 1.8333…, which is a repeating decimal. It can also be written as 1.83̅, where the bar over the 3 indicates that the digit 3 repeats indefinitely.
Explanation
Rational numbers are numbers that can be expressed as a fraction, where the numerator and the denominator are both integers and the denominator is not zero. The number 11/6 is a rational number because it fits this definition. To convert this fraction into decimal form, you simply divide the top number (numerator) by the bottom number (denominator).
In this case, dividing 11 by 6 gives:
- 6 goes into 11 one time (1 × 6 = 6)
- Subtract 6 from 11 to get a remainder of 5
- Add a decimal point and a zero, making it 50
- 6 goes into 50 eight times (8 × 6 = 48)
- Subtract 48 from 50 to get a remainder of 2
- Add another zero to make it 20
- 6 goes into 20 three times (3 × 6 = 18)
- Subtract 18 from 20 to get a remainder of 2 again
This process will continue repeating with the same remainder, leading to the same digit being added to the decimal each time. So the decimal continues as 1.8333…, with the 3 repeating forever. This kind of decimal is known as a repeating decimal.
Repeating decimals are a common feature of rational numbers when the division does not terminate. They are different from terminating decimals, which end after a certain number of digits. In conclusion, 11/6 is written in decimal form as 1.83̅, showing that it repeats and does not end.
