How do you write [tex]$\frac{2}{11}$[/tex] as a decimal?
A. [tex]$0.1 \overline{3}$[/tex]
B. [tex]$0 . \overline{1}$[/tex]
C. [tex]$0.1 \overline{6}$[/tex]
D. [tex]$0 . \overline{18}$[/tex]
Answer (1)
Perform long division to convert the fraction 11 2 to a decimal.
Observe the repeating pattern in the quotient.
Express the result as a decimal with the repeating part indicated by a bar over the repeating digits.
The decimal representation of 11 2 is 0. 18 .
Explanation
Understanding the Problem We need to convert the fraction 11 2 into a decimal. To do this, we will perform long division.
Performing Long Division Let's perform the long division of 2 divided by 11. Since 2 is smaller than 11, we add a decimal point and a zero, making it 2.0.
11 goes into 20 once (1 x 11 = 11), leaving a remainder of 9 (20 - 11 = 9). So, we have 0.1.
We bring down another zero, making it 90. 11 goes into 90 eight times (8 x 11 = 88), leaving a remainder of 2 (90 - 88 = 2). So, we have 0.18.
We bring down another zero, making it 20. 11 goes into 20 once (1 x 11 = 11), leaving a remainder of 9 (20 - 11 = 9). So, we have 0.181.
We bring down another zero, making it 90. 11 goes into 90 eight times (8 x 11 = 88), leaving a remainder of 2 (90 - 88 = 2). So, we have 0.1818.
We can see that the pattern '18' repeats. Therefore, the decimal representation of 11 2 is 0. 18 .
Identifying the Correct Option Comparing our result with the given options, we find that the correct answer is 0. 18 .
Final Answer Therefore, 11 2 = 0. 18 .
Examples
Understanding how to convert fractions to decimals is useful in everyday situations, such as when splitting a bill with friends. For example, if a bill is $2 and you want to split it among 11 people, each person would owe 11 2 of the bill. Converting this to a decimal, each person owes approximately $0.18. This makes it easier to understand and manage the payment.
