# How is「第3位を四捨五入」deconstructed to mean “round up to 2 decimal places”?

I initially translated this sentence to:

If a fraction with less than 2 decimal places is generated, round off to 3 decimal places.

So: 2.1 ≈ 2.100

It felt somewhat off, so I sought for some sample translations for「四捨五入」.

• JP: 。。。小数点第３位を四捨五入して。。。

• EN: ...is rounded off to two decimal places...

So: 2.1 ≈ 2.10

## What?!

Why is it translated this way? Does 「四捨五入」 make the decimal places less than the mentioned number or something else entirely? How do speakers reconcile this?

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Notice the を after 小数第３位? You are not rounding off to the 3rd decimal, you are "promoting or demoting" it. – dainichi May 9 '14 at 3:54
To voters: It would be really helpful if you explain why this question deserves a down-vote. – helix May 9 '14 at 4:54

You're taking the third place (第3位) and you're either throwing it away if it's four or below (四捨) or you add one to the next place if it's five or above (五入).

As a result, the third place is gone, and you're only left with two decimal places.

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I think the problem comes from "小数第２位未満", but not he latter part.

From the sentence, it should mean that a decimal place after the second decimal point is generated. Like:

3.1415 ≈ 3.14

As the decimal places goes further, the actual number it represents becomes smaller. I think this is what 未満 comes from. It means:

when a decimal place that is not big enough to be represented by the the second decimal place is generated, then ...

So, to you question:

Does 「四捨五入」 make the decimal places less than the mentioned number or something else entirely?

No. It does not mean that. snailboat has already given what 「四捨五入」 means. It means to round up. The whole sentence you gave should be translated:

If a fraction with MORE than 2 decimal places is generated, round up to 2 decimal places.

P.S Sorry for the English. Any edit is welcome.

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