Gigabytes per month to Kibibytes per month conversion

How to convert gigabytes per month to kibibytes per month?

To convert from Gigabytes per month (GB/month) to Kibibytes per month (KiB/month), you need to understand the difference between the SI (base 10) and binary (base 2) systems of measurement.

1. Base 10 Conversion: In the base 10 system, 1 Gigabyte (GB) is equal to $10^9$ bytes. 1 byte is equal to $10^3$ Kilobytes (KB). 1 Kilobyte (KB) is equal to $10^3$ bytes. And from bytes, 1 Kilobyte (KB) is equal to 1000 bytes.

   So, we first convert a Gigabyte to Kilobytes: $1 \, \text{GB} = 10^9 \, \text{bytes}$

   Now, convert bytes to Kilobytes: $1 \, \text{GB} = \frac{10^9}{10^3} = 10^6 \, \text{KB}$

   Since 1 Kilobyte (KB) in base 10 is equal to 1000 bytes, we convert it to Kibibytes (KiB) by considering 1 KB = 1000/1024 KiB: $1 \, \text{KB} \approx 0.9765625 \, \text{KiB}$

   Finally, our conversion from 10^6 KB to KiB: $10^6 \, \text{KB} \times 0.9765625 \, \text{KiB/Kilobyte} = 976562.5 \, \text{KiB}$

   Therefore: $1 \, \text{GB/month} \approx 976562.5 \, \text{KiB/month}$

2. Base 2 Conversion: In the base 2 system, 1 Gigabyte (GB) is equal to $2^{30}$ bytes. 1 Kibibyte (KiB) is equal to $2^{10}$ bytes.

   So, we directly convert from Gigabytes to Kibibytes: $1 \, \text{GB} = 2^{30} \, \text{bytes}$

   Convert bytes to Kibibytes: $1 \, \text{GB} = \frac{2^{30}}{2^{10}} = 2^{20} \, \text{KiB}$ $2^{20} = 1048576 \, \text{KiB}$

   Therefore: $1 \, \text{GB/month} = 1048576 \, \text{KiB/month}$

Real-world Examples:

1. 5 GB/month Plan:

   • Base 10: $5 \, \text{GB} \times 976562.5 \, \text{KiB/GB} = 4882812.5 \, \text{KiB/month}$

   • Base 2: $5 \, \text{GB} \times 1048576 \, \text{KiB/GB} = 5242880 \, \text{KiB/month}$

2. 10 GB/month Plan:

   • Base 10: $10 \, \text{GB} \times 976562.5 \, \text{KiB/GB} = 9765625 \, \text{KiB/month}$

   • Base 2: $10 \, \text{GB} \times 1048576 \, \text{KiB/GB} = 10485760 \, \text{KiB/month}$

3. 50 GB/month Plan:

   • Base 10: $50 \, \text{GB} \times 976562.5 \, \text{KiB/GB} = 48828125 \, \text{KiB/month}$

   • Base 2: $50 \, \text{GB} \times 1048576 \, \text{KiB/GB} = 52428800 \, \text{KiB/month}$

These conversions help in visualizing and calculating data plans on different scales in real-world scenarios.