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)
Convert the fraction 11 2 to a decimal by performing long division.
Recognize the repeating pattern in the decimal representation: 0.181818...
Express the repeating decimal using bar notation: 0. 18 .
The decimal representation of 11 2 is 0. 18 .
Explanation
Problem Analysis We are asked to convert the fraction 11 2 into a decimal and choose the correct representation from the given options.
Conversion Method To convert a fraction to a decimal, we perform long division. In this case, we divide 2 by 11.
Performing the Division Performing the division, we find that 11 2 = 0.181818... The digits 18 repeat indefinitely.
Decimal Representation We can represent the repeating decimal 0.181818... as 0. 18 .
Final Answer Selection Comparing our result with the given options, we see that the correct answer is 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 of 2 i ss pl i t am o n g 11 p eo pl e , e a c h p erso n o w es \frac{2}{11}$ of the bill. Converting this to a decimal, we find that each person owes approximately $0.18. This skill is also helpful in cooking, where recipes often use fractional measurements that need to be converted to decimals for precise measuring.
