Substances sometimes shrink when they dry. A silicone sheet dried and over time shrank $-\frac{6}{11}$ inch for every linear foot. Which repeating decimal is equivalent to $-\frac{6}{11}$ ?
A. $-0 . \overline{54}$
B. $-054$
C. $-0.54$
D. $-0.8 \overline{3}$
Answer (1)
Divide 6 by 11 to find the decimal representation.
Recognize the repeating pattern in the decimal.
Apply the negative sign since the original fraction is negative.
Express the repeating decimal as − 0. 54 .
Explanation
Problem Analysis We are given the fraction − 11 6 and asked to find its equivalent repeating decimal representation.
Conversion Method To convert the fraction to a decimal, we perform long division of 6 by 11.
Performing the Division When we divide 6 by 11, we get 0.545454... , where the digits 54 repeat indefinitely.
Applying the Negative Sign Since the original fraction is negative, the decimal representation is − 0.545454... , which can be written as − 0. 54 .
Final Answer Therefore, the repeating decimal equivalent to − 11 6 is − 0. 54 .
Examples
Understanding repeating decimals is useful in various real-life situations, such as when dealing with measurements or calculations that result in fractions. For example, if you are dividing a length of material into equal parts and the division results in a repeating decimal, knowing how to represent and work with these decimals ensures accurate measurements and avoids errors in your calculations. Suppose you need to cut a 6-foot piece of silicone sheet into 11 equal sections. Each section would be 11 6 feet long, which is approximately 0.545454... feet. For practical purposes, you would need to understand this repeating decimal to make accurate cuts.
