Gigabytes per minute to Tebibytes per hour conversion

How to convert gigabytes per minute to tebibytes per hour?

To convert data transfer rates from gigabytes per minute (GB/min) to tebibytes per hour (TiB/hr), you need to take into account both the conversion factors between different time units and between different data size units.

First, let's establish the basics:

1. There are 60 minutes in one hour.
2. I gigabyte (GB) is $10^9$ bytes (base 10).
3. 1 tebibyte (TiB) is $2^{40}$ bytes (base 2).

Base 10 Conversion:

1. Convert 1 GB to bytes: $1 \text{ GB} = 10^9 \text{ bytes}$.
2. Multiply by minutes per hour: $1 \text{ GB/min} \times 60 \text{ min/hr} = 60 \times 10^9 \text{ bytes/hr}$.
3. Convert bytes to tebibytes: $1 \text{ TiB} = 2^{40} \text{ bytes} = 1,099,511,627,776 \text{ bytes}$
4. $60 \times 10^9 \text{ bytes/hr} = \frac{60 \times 10^9 \text{ bytes/hr}}{1,099,511,627,776 \text{ bytes/TiB}} \approx 0.0547 \text{ TiB/hr}$

Base 2 Conversion:

1. Convert 1 GB to Gibibytes (GiB): $1 \text{ GB} = \frac{2^{30}}{10^9} \text{ GiB} \approx 0.9313 \text{ GiB}$
2. Now, calculate the GiB per minute: $1 \text{ GB/min} \approx 0.9313 \text{ GiB/min}$
3. Multiply by minutes per hour: $0.9313 \text{ GiB/min} \times 60 \text{ min/hr} = 55.878 \text{ GiB/hr}$
4. Convert GiB/hr to TiB/hr: $1 \text{ TiB} = 2^{10} \text{ GiB} = 1024 \text{ GiB}$
5. $55.878 \text{ GiB/hr} = \frac{55.878}{1024} \text{ TiB/hr} \approx 0.0546 \text{ TiB/hr}$

Real-world examples:

1. 10 GB/min:

   • Base 10: $10 \text{ GB/min} \approx 0.547 \text{ TiB/hr}$
   • Base 2: $10 \text{ GB/min} \approx 0.546 \text{ TiB/hr}$

2. 50 GB/min:

   • Base 10: $50 \text{ GB/min} \approx 2.735 \text{ TiB/hr}$
   • Base 2: $50 \text{ GB/min} \approx 2.731 \text{ TiB/hr}$

3. 100 GB/min:

   • Base 10: $100 \text{ GB/min} \approx 5.47 \text{ TiB/hr}$
   • Base 2: $100 \text{ GB/min} \approx 5.463 \text{ TiB/hr}$

These conversions illustrate how you can transform data transfer rates from gigabytes per minute to tebibytes per hour using different bases.