I read that, in the USA, one billion is considered to be 1×109 (1 000 000 000).
In Mexico, it's 1×1012 (1 000 000 000 000).
Are both values used by American English speakers?
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One billion is 10^9. One trillion is 10^12. This use is standard for English speakers in the USA, Australia, Canada and in the UK. The "short" scale was adopted by the UK government in 1974, but some older speakers may prefer the long scale.
There is the potential for confusion, especially among speakers of other languages (Spanish in the USA or French in Canada) who use the long scale in their native language, so it would not be impolite to ask to confirm.