Oxford Advanced American Dictionary

Definition of that conjunction from the Oxford Advanced Learner's Dictionary

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that

conjunction
 
that pronunciation English ðət that pronunciation American ðət
rare strong formthat pronunciation English ðæt that pronunciation American ðæt
1 used after some verbs, adjectives and nouns to introduce a new part of the sentenceShe said (that) the story was true.It's possible (that) he has not received the letter.The fact (that) he's older than me is not relevant.
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In spoken and informal written English that is usually left out after reporting verbs and adjectives. It is less often left out after nouns.
2 so… that… used to express a resultShe was so tired (that) she couldn't think straight.
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In informal English that is often left out.
3 (literary) used for expressing a hope or a wishOh that I could see him again!