You wouldn't be blamed for thinking that the Thai numbers were written in the international format as standard: 1, 2, 3, 4, 5, etc – because Thais (generally) write using the same numbers we do, and signs all over Thailand feature the same. But what you may not have noticed is the real Thai numeric system, which is still very much in use.
It's quite easy to get by in Thailand without knowing how to write Thai numbers because Thais will understand what you mean when you write an international number on paper (there will be exceptions with some elders in rural areas). But all the same, if you are learning Thai then you really should get to grips with the Thai numerical system, not just for general knowledge but so you can increase your understanding of signs and other labelling around the country.
A common place you will see the Thai numerical system in use is on the back of motorbike taxi jackets. Each taxi rank has a number attached to its employees, according to the soi (road)/area. This presents a great way to practice learning your Thai numbers. Next time you are walking down the street, see if you can read the Thai number on the back of each motorbike taxi driver you see.
Here are the Thai numbers with phonetic translations: