Gigabytes to Tebibytes conversion

How to convert gigabytes to tebibytes?

To explain how to convert 1 Gigabyte to Tebibytes, you need to understand the difference between the base 10 (decimal) and base 2 (binary) systems.

GB to TiB in Base 10 (Decimal System)

In the decimal system, the prefix "Giga" means $10^9$ bytes and "Tebi" means $2^{40}$ bytes. However, since we're converting base 10 GB to TiB, we won't strictly use the base 2 conversion factors.

1 Gigabyte (GB) = $10^9$ bytes

1 Tebibyte (TiB) = $2^{40}$ bytes = 1,099,511,627,776 bytes

To convert:

$\text{1 GB (base 10) in TiB} = \frac{1 \times 10^9 \text{ bytes}}{1,099,511,627,776 \text{ bytes per TiB}} \approx 9.094947 \times 10^{-4} \text{ TiB}$

GB to TiB in Base 2 (Binary System)

In the binary system, the conversion is more straightforward since both GB and TiB are based on powers of 2.

1 Gigabyte (GB) = $2^{30}$ bytes = 1,073,741,824 bytes

1 Tebibyte (TiB) = $2^{40}$ bytes = 1,099,511,627,776 bytes

To convert:

$\text{1 GB (base 2) in TiB} = \frac{1,073,741,824 \text{ bytes}}{1,099,511,627,776 \text{ bytes per TiB}} \approx 9.536743 \times 10^{-4} \text{ TiB}$

Real-World Examples for Other Quantities of Gigabytes

Let's apply these conversions to some more quantities of Gigabytes.

In Base 10 (Decimal System)

1. 10 GB to TiB: $\text{10 GB} = 10 \times 10^9 \text{ bytes} / 1,099,511,627,776 \text{ bytes per TiB} \approx 0.009094947 \text{ TiB}$

2. 500 GB to TiB: $\text{500 GB} = 500 \times 10^9 \text{ bytes} / 1,099,511,627,776 \text{ bytes per TiB} \approx 0.454747 \text{ TiB}$

3. 1 TB to TiB: Since 1 Terabyte (TB) = 1,000 Gigabytes (GB): $\text{1,000 GB} = 1,000 \times 10^9 \text{ bytes} / 1,099,511,627,776 \text{ bytes per TiB} \approx 0.909495 \text{ TiB}$

In Base 2 (Binary System)

1. 10 GB to TiB: $\text{10 GB} = 10 \times 1,073,741,824 \text{ bytes} / 1,099,511,627,776 \text{ bytes per TiB} \approx 0.009536743 \text{ TiB}$

2. 500 GB to TiB: $\text{500 GB} = 500 \times 1,073,741,824 \text{ bytes} / 1,099,511,627,776 \text{ bytes per TiB} \approx 0.476837 \text{ TiB}$

3. 1 TB to TiB: Since 1 Terabyte (TB) = 1,000 Gigabytes (GB): $\text{1,000 GB} = 1,000 \times 1,073,741,824 \text{ bytes} / 1,099,511,627,776 \text{ bytes per TiB} \approx 0.953674 \text{ TiB}$

Conclusion

The conversions show slightly different values depending on whether you are using base 10 or base 2:

• Base 10: 1 GB ≈ 9.094947 × 10^-4 TiB
• Base 2: 1 GB ≈ 9.536743 × 10^-4 TiB

These differences arise from the different definitions of GB in decimal and binary systems.