Chapter 2, Problem 5E

a)

Explanation of Solution

Converting 20012 base 3 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 3.

$\begin{array}{l}{\text{2 x 3}}^{\text{0}}\text{= 2}\\ {\text{1 x 3}}^1\text{= 3}\\ {\text{0 x 3}}^2\text{= 0}\\ {\text{0 x 3}}^3\text{= 0}\end{array}$

${\text{2 x 3}}^4\text{= 162}$

Step 2: Add all the values to get the equivalent base 10 value

b)

Explanation of Solution

Converting 4103 base 5 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 5.

$\begin{array}{l}{\text{3 x 5}}^{\text{0}}\text{= 3}\\ {\text{0 x 5}}^1\text{= 0}\\ {\text{1 x 5}}^2\text{= 25}\\ {\text{4 x 5}}^3\text{= 500}\end{array}$

Step 2: Add all the values to get the equivalent base 10 value

c)

Explanation of Solution

Converting 3236 base 7 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 7.

$\begin{array}{l}{\text{6 x 7}}^{\text{0}}\text{= 6}\\ {\text{3 x 7}}^1\text{= 21}\\ {\text{2 x 7}}^2\text{= 98}\\ {\text{3 x 7}}^3\text{= 1029}\end{array}$

Step 2: Add all the values to get the equivalent base 10 value

d)

Explanation of Solution

Converting 1378 base 9 to base 10:

Step 1: Write the given number from left to the right and multiply the number with the base 9.

$\begin{array}{l}{\text{8 x 9}}^{\text{0}}\text{= 8}\\ {\text{7 x 9}}^1\text{= 63}\\ {\text{3 x 9}}^2\text{= 243}\\ {\text{1 x 9}}^3\text{= 729}\end{array}$

Step 2: Add all the values to get the equivalent base 10 value