Question

question 2 of 8 select the two correct answers. maya is designing a new bookshelf and needs to divide wooden planks into equal sections. she takes a 7-foot-long plank and divides it into 6 equal parts. she wants to know the exact length of each section in decimal form. select the correct decimal representations of the result. options: 1.(overline{16}), 1.1666..., 1.161616..., (1.1overline{6}), 1.16

Explanation:

Step1: Calculate the length of each section

To find the length of each section, we divide the total length of the plank (7 feet) by the number of equal parts (6). So we perform the division \(7\div6\).
\(7\div6 = 1.1666\cdots\) (where 6 repeats infinitely) and also can be represented as a repeating decimal with the bar over 6, i.e., \(1.1\overline{6}\), and the non - terminating decimal \(1.1666\cdots\).

Step2: Analyze each option

• Option \(1.1\overline{6}\): This is the repeating decimal representation of \(7\div6\) where 6 repeats, so this is correct.
• Option \(1.1666\cdots\): This is the non - terminating decimal form of \(7\div6\), so this is correct.
• Option \(1.\overline{16}\): This represents a decimal where 16 repeats (\(1.161616\cdots\)), which is not equal to \(7\div6\), so this is incorrect.
• Option \(1.161616\cdots\): This is a repeating decimal with 16 repeating, not equal to \(7\div6\), so this is incorrect.
• Option \(1.16\): This is a terminating decimal and \(1.16

eq1.1666\cdots\), so this is incorrect.

Answer:

\(1.1\overline{6}\), \(1.1666\cdots\)