度
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度 is a notch on a scale
The picture A scale marked in notches, like a thermometer. Each time something happens, the mark climbs one notch; all that changes is how far it has climbed.
Where the picture shows up in 度
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the needle at zero
沖縄には一度も行ったことがありません。
okinawa ni wa ichido mo itta koto ga arimasen
I've never once been to Okinawa.
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the next notch
今度、飲みに行きましょう。
kondo, nomi ni ikimashō
Let's go for a drink sometime soon.
今度 can mean 'this time' or 'next time'. If it hasn't happened yet, it usually means next time.
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degrees of heat
熱が三十八度あります。
netsu ga sanjūhachi-do arimasu
My temperature is 38.
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one notch more
すみません、もう一度お願いします。
sumimasen, mō ichido onegai shimasu
Sorry — one more time, please.
回 counts repetitions flatly; 度 carries the feel of having lived through them. 「週に三回」 would sound odd with 度.
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past the last notch
冗談も度が過ぎますよ。
jōdan mo do ga sugimasu yo
That joke has gone too far.