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日本の記録は2分53秒89で、オリンピックの新しい記録になりました。
The Japanese result was 2 minutes 53.89 seconds and became a new Olympic record.

I haven't seen this way of writing a decimal number before, by putting the unit of measurement between the integer and fractional part. Can this be done with measurements other than time e.g. can I write 1.5km as 1キロ5? Are there any contexts where it is more/less appropriate to write it like this?

4

I think this convention is almost specific to sport or racing contexts. Outside such contexts you should usually say 53.89秒 (ごじゅうさんてんはちきゅうびょう). Just to make sure, 53秒89 is read ごじゅうさんびょうはちきゅう, not はちじゅうきゅう, as if 秒 were the decimal mark.

According to 陸上競技アナウンサーのしおり(2017年度版), sub-meter lengths are officially written similarly but pronounced differently, presumably because センチメートル is a well-known unit:

  • 8m40 はちメートルよんじゅう (not はちメートルよんれい or よんぜろ)
  • 8m03 はちメートルさん (not はちメートルれいさん or ぜろさん)

But I personally feel the readings in parentheses are not unnatural. Again, outside sport contexts you should use "8.4m" (はってんよんメートル) or "8m40cm" (はちメートルよんじゅっセンチ), although はちメートルよんじゅう would be safely understood.

記録の読み方

① 時間

  • 電気計時の秒未満の数字は一文字一文字で読む。
    例) 10 秒 22……「にじゅうに」ではなく、「にいにい」と読む。
  • 十秒、十分の単位が「0」の場合
    例) 2 分 05 秒 27…… 十秒の単位を「れい 5 秒」とは言わず、分と秒の間に「一呼吸」入れて「5 秒」と言う。
    例) 2 分 00 秒 00…… 秒の単位は「れい・れい」秒ではなく「れい」秒。秒単位未満は「れい・れい」と言う。
    例) 2 時間 01 分 06 秒……分の単位を「れい 1 分」とは言わず、時間と分の間に「一呼吸」入れて「1 分」、秒の単位を「れい 6 秒」とは言わず、「6 秒」と言う。

② 距離や高さ

  • 「m未満」の十の位が「0」の場合
    例)2m03………「2mれい 3」とは言わず、「2m」の後に「一呼吸」入れて、「3」と言う(言い切る)。
    例)2m00………「2mれい・れい」「2mちょうど」とは言わず、「2mれい」と言う(言い切る)。
  • Apologies for the late tick. I thought I'd done it, but I just noticed I hadn't. – user3856370 Feb 25 '18 at 15:53
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I think that this is exclusive to milliseconds, where it is understood from the context.

1.5km would be 1.5キロ or 1キロ500メートル. As opposed to time measurement, the metric system is highly conducive to decimals, I don't see many situations that they wouldn't be used.

One mile, 400 feet, 9 inches would be 1マイル400フィート9インチ. As inches can be assumed, but not with the same level of certainty as the millisecond example, it would not be left off.

TL;DR I believe it is only for time.

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