91Ó°ÊÓ

Express each number in decimal notation. \(1 \times 10^{5}\)

Find each product. \((-17)(-1)\)

Express each repeating decimal as a quotient of integers. If possible, reduce to lowest terms. \(0 . \overline{1}\)

Find the greatest common divisor of the numbers. 96 and 212

Perform the indicated operation. Simplify the answer when possible. \(\sqrt{63}-\sqrt{28}\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=3\)

Express each number in decimal notation. \(1 \times 10^{8}\)

Shown in the figure is a 7-hour clock and the table for clock addition in the 7-hour clock system. $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \oplus & \mathbf{0} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \hline \mathbf{0} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \mathbf{1} & 1 & 2 & 3 & 4 & 5 & 6 & 0 \\ \hline \mathbf{2} & 2 & 3 & 4 & 5 & 6 & 0 & 1 \\ \hline \mathbf{3} & 3 & 4 & 5 & 6 & 0 & 1 & 2 \\ \hline \mathbf{4} & 4 & 5 & 6 & 0 & 1 & 2 & 3 \\ \hline \mathbf{5} & 5 & 6 & 0 & 1 & 2 & 3 & 4 \\ \hline \mathbf{6} & 6 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \end{array} $$ a. How can you tell that the set \(\\{0,1,2,3,4,5,6\\}\) is closed under the operation of clock addition? b. Verify one case of the associative property: \((3 \oplus 5) \oplus 6=3 \oplus(5 \oplus 6)\) c. What is the identity element in the 7-hour clock system? d. Find the inverse of each element in the 7-hour clock system. e. Verify two cases of the commutative property: \(4 \oplus 5=5 \oplus 4\) and \(6 \oplus 1=1 \oplus 6\)

Shown in the figure is an 8-hour clock and the table for clock addition in the 8-hour clock system. $$ \begin{array}{|l|l|l|l|l|l|l|l|l|} \hline \oplus & \mathbf{0} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} \\ \hline \mathbf{0} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \mathbf{1} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 0 \\ \hline \mathbf{2} & 2 & 3 & 4 & 5 & 6 & 7 & 0 & 1 \\ \hline \mathbf{3} & 3 & 4 & 5 & 6 & 7 & 0 & 1 & 2 \\ \hline \mathbf{4} & 4 & 5 & 6 & 7 & 0 & 1 & 2 & 3 \\ \hline \mathbf{5} & 5 & 6 & 7 & 0 & 1 & 2 & 3 & 4 \\ \hline \mathbf{6} & 6 & 7 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \mathbf{7} & 7 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \end{array} $$ a. How can you tell that the set \(\\{0,1,2,3,4,5,6,7\\}\) is closed under the operation of clock addition? b. Verify one case of the associative property: $$ (4 \oplus 6) \oplus 7=4 \oplus(6 \oplus 7) \text {. } $$ c. What is the identity element in the 8-hour clock system? d. Find the inverse of each element in the 8-hour clock system. e. Verify two cases of the commutative property: \(5 \oplus 6=6 \oplus 5\) and \(4 \oplus 7=7 \oplus 4\).

Express each number in decimal notation. \(7.9 \times 10^{-1}\)