Notice that 1/7 = 0.142857, 2/7 = 0.285714, 3/7 = 0.428571, 4/7 = 0.571428, 5/7 = 0.714285, and 6/7 = 0.857142. Complete parts (a) through (c) below.
a. Describe a common property that all of these repeating decimals share. Choose the correct common property below.
A. They each have six-digit repetends using each of the digits 1, 2, 4, 5, 7, 8 exactly once in different cyclic order.
B. They each have seven-digit repetends using each of the digits 0, 1, 2, 4, 5, 7, 8 exactly once in different cyclic orders.
C. They each have six-digit repetends using each of the digits 1, 2, 4, 5, 7, 8 exactly once in the same cyclic order.
D. They each have seven-digit repetends using each of the digits 0, 1, 2, 4, 5, 7, 8 exactly once in different cyclic orders.
b. How could you quickly find the answers for the decimal expansions of the five fractions above? Select all that apply.
A. The patterns of the digits are cyclic.
B. The first digit of the repetend increases as the fraction increases.