Questions: There are megabytes in a terabyte. 2^20 2^40 2^30 2^10

Transcript text: There are $\qquad$ megabytes in a terabyte. $2^{20}$ $2^{40}$ $2^{30}$ $2^{10}$

Solution

Solution Steps

To determine how many megabytes are in a terabyte, we need to understand the relationship between bytes, kilobytes, megabytes, gigabytes, and terabytes. Specifically, we need to convert terabytes to megabytes using the fact that:

1 kilobyte (KB) = $2^{10}$ bytes
1 megabyte (MB) = $2^{10}$ kilobytes
1 gigabyte (GB) = $2^{10}$ megabytes
1 terabyte (TB) = $2^{10}$ gigabytes

Thus, 1 terabyte is $2^{10} \times 2^{10} \times 2^{10}$ megabytes.

Step 1: Understanding the Conversion Factors

To determine how many megabytes are in a terabyte, we need to understand the hierarchical relationship between different units of digital storage. Specifically:

$1 \text{ KB} = 2^{10} \text{ bytes}$
$1 \text{ MB} = 2^{10} \text{ KB}$
$1 \text{ GB} = 2^{10} \text{ MB}$
$1 \text{ TB} = 2^{10} \text{ GB}$

Step 2: Converting Terabytes to Megabytes

To convert 1 terabyte to megabytes, we multiply the conversion factors: \[ 1 \text{ TB} = 2^{10} \text{ GB} \times 2^{10} \text{ MB/GB} \times 2^{10} \text{ KB/MB} \]

Step 3: Simplifying the Expression

Simplify the expression using the properties of exponents: \[ 1 \text{ TB} = 2^{10} \times 2^{10} \times 2^{10} \text{ MB} = 2^{30} \text{ MB} \]

Step 4: Calculating the Value

Calculate the value of $2^{30}$: \[ 2^{30} = 1073741824 \]