The Number System in the Korean Language can confuse you since there are various forms and types of them. It is mainly related to the following matters.
1. A matter of the origins of the words
There are two origins for Korean words: pure Korean words and Chinese-origin words(Sino-Korean words).
The usage of the two is different, which is the point you have to memorize.
2. A matter of parts of speech
There are two kinds of parts of speech that refer to numbers.
1) Numerals
Along with nouns and pronouns, they usually play roles as subjects, objects, or complements in sentences with particles attached behind them.
(1) Quantifier
Quantifiers are used when you count the number.
Pure Korean words are used in almost every context and especially when you count numbers that are under 100.
하나(1), 둘(2), 셋(3), 넷(4), 다섯(5), 여섯(6), 일곱(7), 여덟(8), 아홉(9), 열(10) ...
우리 둘은 친한 친구이다. The two of us are close friends.
Sino-Korean words are used in calculation and mathematics, or when the number is over 100.
일(1), 이(2), 삼(3), 사(4), 오(5), 육(6), 칠(7), 팔(8), 구(9), 십(10) ...
일 더하기 이는 삼이다. One plus two equals three.
(2) Ordinal
Ordinals are used when you refer to the order.
Koreans use usually pure Korean words for ordinal numbers. Except for 첫째(first), they are easy to make. Just add the suffix -째 behind the quantifiers.
첫째(1st), 둘째(2nd), 셋째(3rd), 넷째(4th), 다섯째(5th), 여섯째(6th), 일곱째(7th), 여덟째(8th), 아홉째(9th), 열째(10th)
둘째로 중요한 것은 건강이다. The second important thing is health.
Sino-Korean words are not that frequently used.
제일(1st), 제이(2nd), 제삼(3rd), 제사(4th), 제오(5th), 제육(6th), 제칠(7th), 제팔(8th), 제구(9th), 제십(10th)
이곳은 나에게 제이의 고향이다. This place is my second hometown.
2) Numeral Determiners
Numeral determiners are used in order to modificate or limit the meaning of nouns. They always need a noun behind them and cannot be attached by particles.
They are also divided into pure Korean words and Sino-Korean words. The forms are identical to each numeral except for pure Korean words for 1, 2, 3, 4, and 20.
Pure Korean words are used in all contexts.
한(1), 두(2), 세(3), 네(4), 다섯(5), 여섯(6) ...
저 두 소년은 친구다. That two boys are friends.
첫째(1), 둘째(2), 셋째(3), 넷째(4) ...
나의 둘째 딸은 상냥하다. My second daughter is sweet.
Sino-Korean words are usually used before Sino-Korean measurement nouns(단위명사).
일(1), 이(2), 삼(3), 사(4), 오(5), 육(6) ...
군인 일 명이 근무 중이다. A soldier is on duty.
삼 년이 지났다. Three years have passed.
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