How do you write [tex]$\frac{13}{18}$[/tex] as a decimal?
A. [tex]$0 . \overline{2}$[/tex]
B. [tex]$0 . \overline{7}$[/tex]
C. [tex]$0.7 \overline{2}$[/tex]
D. [tex]$0.6 \overline{1}$[/tex]
Answer (2)
Convert the fraction 18 13 to a decimal using long division.
Observe that the result of the division is 0.72222... .
Identify the repeating digit and write the decimal as 0.7 2 .
The fraction 18 13 as a decimal is 0.7 2 .
Explanation
Understanding the Problem We need to convert the fraction 18 13 to a decimal. To do this, we perform long division.
Performing the Division Performing the division, we get 13 ÷ 18 = 0.72222... .
Identifying the Repeating Decimal We can see that the digit 2 repeats indefinitely. Therefore, we can write the decimal as 0.7 2 .
Selecting the Correct Option Comparing this result with the given options, we find that the correct option is 0.7 2 .
Final Answer Therefore, the fraction 18 13 as a decimal is 0.7 2 .
Examples
Understanding how to convert fractions to decimals is useful in everyday situations, such as when calculating proportions or percentages. For example, if you want to determine what percentage of your monthly budget is allocated to rent, and your rent is 18 13 of your total budget, converting this fraction to a decimal (approximately 0.7222) allows you to easily express it as a percentage (72.22%). This makes it easier to understand and compare different parts of your budget.
To convert 18 13 to a decimal, we perform long division and find that it equals 0.7 2 , which shows that 2 repeats indefinitely. The correct answer is C. 0.7 2 .
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