一点儿/有点儿
yìdiǎnr / yǒudiǎnr
Move a bit from the front to the back and a complaint turns into a request
The picture One tiny grain. Hold it out and ask for it and you get 一点儿 after the adjective; find it already stuck to you and grumble, and you get 有点儿 in front. 一点儿 is a small amount; 一下 is a short while. Hang on a moment is 等一下, never 等一点儿.
Where the picture shows up in 一点儿/有点儿
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a little less, please
盐少放一点儿。
yán shǎo fàng yìdiǎnr
Go easy on the salt.
Holding your palm out in front of the salt shaker to mark off just this much
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a little that is already there
这件衣服有点儿贵。
zhè jiàn yīfu yǒudiǎnr guì
This one's a bit pricey.
Fingering a sleeve in a clothes shop, flipping the price tag over, and your eyebrows going up
有点儿 almost always leads into something unwelcome; 有点儿便宜 sounds broken.
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a little more of it, please
你能说慢一点儿吗?
nǐ néng shuō màn yìdiǎnr ma
Could you speak a bit more slowly?
Pressing your palm downward in the air to ask someone's speech to slow a notch
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a little stuck to me
我今天有点儿累,先回去了。
wǒ jīntiān yǒudiǎnr lèi, xiān huíqu le
I'm a bit tired today, I'll head home first.
Leaning on the strap on the train home with your shoulders sunk a little
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a little once measured
今天比昨天冷一点儿。
jīntiān bǐ zuótiān lěng yìdiǎnr
It's a bit colder today than yesterday.
Yesterday's and today's thermometers side by side, a finger on the one-notch gap between them
After a comparison, 一点儿 means by that much more.
All of it in one picture
Asking for less salt and asking someone to slow down are both 一点儿 — your palm out, requesting a grain. The coat being pricey and today being tiring are both 有点儿 — the grain already stuck to you, and you want it off. And a bit colder than yesterday is 一点儿 again: measured out, the gap comes to one notch. The same tiny grain either way; it goes after the adjective when you are asking for it, and in front when it has already landed on you.