One tebibyte is exactly 1.099511627776 terabytes, since a tebibyte is 2⁴⁰ bytes and a terabyte is 10¹². The ten per cent gap at this prefix is where the decimal-binary disagreement stops being a curiosity and starts appearing on invoices.
About the units
The tebibyte is 1,099,511,627,776 bytes, defined by the IEC in 1998 alongside the rest of the binary prefix family. Its decimal namesake, the terabyte, is a flat 10¹² bytes. The accumulated difference is 1.024⁴, just under ten per cent, and it grows by another 2.4 per cent with each prefix above. This is the scale at which enterprise storage is bought and cloud capacity is billed, and where a contract that says only TB without specifying the convention leaves roughly a tenth of the capacity undefined.
The exact factor
The exact value is 2⁴⁰ ÷ 10¹² = 1.099511627776. Going the other way, a terabyte is 0.909494701772928 tebibytes. The practical consequence: a storage system sold as 100 TB provides 90.9 TiB as reported by most operating systems, and a backup plan built on the larger number will fall about nine terabytes short. Filesystem overhead and redundancy reduce usable capacity further, but those are separate deductions and should be calculated after the unit conversion, not conflated with it.
Where you meet this conversion
Enterprise storage procurement, cloud volume provisioning and backup capacity planning. AWS, Azure and Google all specify block storage in GiB or TiB while marketing pages often say GB and TB, so the same service has two published sizes. RAID array capacity, deduplication ratios and snapshot retention calculations all depend on getting the unit right, and a nine per cent error at this scale is a budget item rather than a rounding detail.