Chapter 4.5, Problem 40E

a.

To determine

To find the number of kilobytes in a megabyte.

Answer to Problem 40E

  ${10}^3$

Explanation of Solution

Given information:The table given in the question mentions that 1 unit of a megabyte consists of ${10}^6$ bytes. The table also mentions that 1 unit of a kilobyte comprises of ${10}^3$ bytes.

Formula used: $\frac{x^a}{x^b}=x^{a-b}$

Calculation:

As per the given problem, 1 megabyte = ${10}^6$ bytes

Also, 1 kilobyte $={10}^3$ bytes

Hence, to find out the number of kilobytes in 1 megabyte, divide the number of bytes in one megabyte by the number of bytes in 1 kilobyte.

=> Number of kilobytes in a megabyte= $\frac{{10}^6}{{10}^3}$

  $={10}^{6-3}$

  $={10}^3$ megabytes

b.

To determine

To find the number of gigabytes in a petabyte.

Answer to Problem 40E

  ${10}^6$

Explanation of Solution

Given information: The table given in the question mentions that 1 unit of a gigabyte consists of ${10}^9$ bytes. The table also mentions that 1 unit of a petabyte comprises of ${10}^{15}$ bytes.

Formula used: $\frac{x^a}{x^b}=x^{a-b}$

Calculation:

As given in the question, 1 petabyte = ${10}^{15}$ bytes

Also, 1 gigabyte = ${10}^9$ bytes

=> Number of gigabytes in a petabyte= $\frac{{10}^{15}}{{10}^9}$

  $={10}^{15-9}$

  $={10}^6$ megabytes

c.

To determine

To findthe number of megabytes in a petabyte.

Answer to Problem 40E

  ${10}^9$

Explanation of Solution

Given information: The table given in the question mentions that 1 unit of a megabyte consists of ${10}^6$ bytes. The table also mentions that 1 unit of a petabyte comprises of ${10}^{15}$ bytes.

Formula used: $\frac{x^a}{x^b}=x^{a-b}$

Calculation:

As given in the question, 1 petabyte = ${10}^{15}$ bytes

Also, 1 megabyte = ${10}^6$ bytes

=> Number of gigabytes in a petabyte= $\frac{{10}^{15}}{{10}^6}$

  $={10}^{15-6}$

  $={10}^9$ megabytes