Question

If a DVD can store 4.7 gigabytes (GB) of data, and a computer hard disk has a capacity of 1.5 terabytes (TB), how many DVDs of data can be loaded onto the hard disk?

Short answer

The hard disk can hold data from 326 DVDs.

Step-by-step solution

Convert Hard Disk Capacity to Gigabytes

The hard disk capacity is given in terabytes (TB) and we need to convert this to gigabytes (GB) because the DVD capacity is in gigabytes. We know that 1 TB is equal to 1024 GB. Therefore, the hard disk capacity in gigabytes is: 1.5 TB = 1.5 * 1024 GB = 1536 GB.

Calculate DVDs Needed

Now that both the DVD storage capacity and the hard disk capacity are in the same units (gigabytes), we can calculate how many DVDs of data can be loaded onto the hard disk. We divide the total hard disk capacity by the amount of data one DVD can hold: Number of DVDs = Total hard disk capacity / DVD capacity = 1536 GB / 4.7 GB/DVD.

Perform the Calculation

Perform the division from Step 2: \( \frac{1536}{4.7} \approx 326.38 \). Since the number of DVDs must be a whole number, and we can't use a fraction of a DVD, round down to the nearest whole number to find that 326 DVDs can be loaded.

Key concepts

Unit Conversion

When dealing with data storage capacities, different units may be used, such as gigabytes (GB) and terabytes (TB). It is important to have a clear understanding of unit conversion because it allows us to compare and calculate storage capacities more effectively. Units can vary significantly, so converting them accurately is crucial.

To convert from one unit to another, such as from terabytes to gigabytes, we must understand the conversion factor between these units. Here, 1 terabyte is equal to 1024 gigabytes. Therefore, to convert terabytes into gigabytes, multiply the number of terabytes by 1024.

For example, if we have a hard disk with a capacity of 1.5 TB, we can find its equivalent in gigabytes by calculating:

• Hard disk capacity (in TB) = 1.5
• Conversion factor from TB to GB = 1024
• Capacity in GB = 1.5 * 1024 = 1536 GB

Understanding unit conversion is essential for tasks such as adding or transferring data storage units with different capacities.

DVD Storage

Digital Versatile Discs, or DVDs, are a common form of data storage. They are used for various purposes such as storing entertainment media, software, and personal data. DVDs have a fixed storage capacity, which is usually 4.7 gigabytes for a standard single-layer disc.

Knowing the storage capacity of a DVD is important when you need to plan how much data you can store on it. When transferring data from other storage mediums, such as a hard disk, it is essential to understand this limitation so you do not attempt to load more data than the DVD can contain.

For example, if a task requires moving data from a hard disk to DVDs, you must calculate the number of DVDs required, considering their capacity limits. If a DVD can hold 4.7 GB of data, exceeding this could result in data not fitting properly or needing additional DVDs. So it's crucial to precisely manage what and how much can be stored on them.

Data Loading Analysis

Analyzing how data can be loaded onto different storage devices involves understanding the total capacity available and comparing it with the storage needs or limits of specific mediums like DVDs. This analysis helps in determining the number of units, like DVDs, required to store or back up all the desired data.

We start by ensuring that all capacities are in the same units for a fair comparison. This typically involves converting storage quantities to gigabytes (GB) since it matches the DVD capacity commonly used in calculations.

In our scenario, after converting a hard disk’s capacity to gigabytes, we perform a division to see how many DVDs are necessary. The arithmetic looks like this:

• Total hard disk capacity in GB = 1536
• One DVD can hold = 4.7 GB
• Number of DVDs needed = 1536 / 4.7
• This results in approximately 326.38 DVDs

Since it's impossible to use a portion of a DVD, we round down to the nearest whole number, resulting in 326 DVDs required. This technique helps in planning efficiently to ensure adequate storage resources are available.