Question

If a USB flash drive can store 16 gigabytes (GB) of data, and a computer hard disk has a capacity of 2.0 terabytes (TB), how many flash drives of data can be loaded onto the hard disk?

Short answer

128 flash drives can be loaded onto the hard disk.

Step-by-step solution

Convert Units

First, we need to convert the capacities to the same unit to make comparisons easier. Recall that 1 TB (terabyte) is equal to 1024 GB (gigabytes). Therefore, we convert the computer hard disk capacity from terabytes to gigabytes: \(2.0 \text{ TB} = 2.0 \times 1024 \text{ GB} = 2048 \text{ GB}\).

Calculate the Number of Flash Drives

Now, we will determine how many 16 GB flash drives can fit into 2048 GB. This can be done by dividing the total capacity of the hard disk by the capacity of one flash drive: \(\frac{2048 \text{ GB}}{16 \text{ GB}} = 128\).

Interpret the Result

The result of the division tells us the number of 16 GB flash drives required to fill the 2.0 TB hard disk. The operation gives us an exact integer, so the entire space of the hard disk (2048 GB) can be used to store data from the flash drives without leaving unused space.

Key concepts

Data Storage

Understanding data storage is crucial when dealing with technological devices like USB flash drives and computer hard disks. The capacity of these storage devices is generally expressed in terms of bytes, with larger units like gigabytes (GB) and terabytes (TB) being commonly used.

• Byte Basics: A byte is a basic unit of data storage, consisting of 8 bits.
• Hierarchy of Units: Moving up from bytes, we have kilobytes (KB), megabytes (MB), gigabytes (GB), and terabytes (TB). Each step up represents a multiplication by 1024 (e.g., 1 KB = 1024 bytes).
• Flash Drives and Hard Disks: A USB flash drive is portable and typically has less storage capacity compared to a computer hard disk. Hard disks are permanent storage units found in computers, providing larger storage due to their size and integration with the system.

By comprehensively understanding these storage units, we can better manage, compare, and convert storage capacities for efficient data handling.

Problem Solving Steps

When tackling problems that involve unit conversions or capacity questions, it's beneficial to follow a structured approach. Here are clear steps demonstrated through the given exercise:

• Step 1: Convert Units
  Start by ensuring all quantities are in compatible units. In this exercise, converting the hard disk's 2.0 TB to GB makes data easier to compare. Always remember that 1 TB = 1024 GB.
• Step 2: Solve the Problem Mathematically
  Once units are uniform, perform the necessary mathematical operations. Here, dividing the total storage (2048 GB) by the storage of one flash drive (16 GB) calculates how many flash drives can fill the hard disk.
• Step 3: Interpret the Result
  After calculating, interpret the number logically. In this case, an integer result (128) indicates whole flash drives perfectly fit without any leftover space.

These steps ensure clarity and accuracy in problem-solving scenarios, especially in technical contexts.

Mathematical Conversion

Mathematical conversions are essential in chemistry and technology to translate quantities into more comparable forms. Here's how it ties into our storage problem:

• Why We Convert: Different topics and devices often use various units. Converting allows straightforward comparisons, as seen with GB and TB in data storage.
• Conversion Method: Identify the conversion factor (e.g., 1024 for GB to TB) and apply it systematically. This factor acts as a bridge between units, facilitating smooth transitions.
• Performing the Conversion: Use multiplication or division, as shown in converting 2.0 TB to 2048 GB. The understanding of these operations is paramount in performing accurate conversions.

In essence, mastering mathematical conversions is vital to handle diverse problems, offering utility beyond academic settings into real-world applications.