How do you know which pronunciation is the right one when using Rikaikun?

[panlanc]

For this word 万能, it shows both ばんのう and まんのう.

左腕 = さわん、ひだりうで。

全治 ＝ぜんじ、ぜんち。

尻尾 しっぽ、しりお

 

[Toritoribe]

You can check it in dictionaries.

万能 ばんのう

Other forms
万能 【まんのう】
Notes
まんのう: Out-dated or obsolete kana usage.

万能 - Jisho.org

jisho.org

尻尾 しっぽ

Other forms
尻尾 【しりお】
Notes
しりお: Out-dated or obsolete kana usage.

尻尾 - Jisho.org

jisho.org

"Other forms" or "⇒(= refer to ぜんち)" shows that ぜんじ is not the common one.
全治 ぜんち

Other forms
全治 【ぜんじ】

全治 - Jisho.org

jisho.org

ぜんじ【全治】 の解説
［名］(スル)⇒ぜんち（全治）

goo

NTTドコモが運営するポータルサイト「goo」。今話題のニュースやドコモのキャンペーン、サービス紹介などお役立ちコンテンツを展開しています。

dictionary.goo.ne.jp

Sometimes the meaning differs depending on the reading.
左腕 さわん
2. left-handed (baseball pitcher) Only applies to さわん

左腕 - Jisho.org

jisho.org

右腕 みぎうで
2. right-hand man; right hand; right-hand person Only applies to みぎうで
3. right-handed pitcher Baseball term, Only applies to うわん

右腕 - Jisho.org

jisho.org

 

[panlanc]

Unfortunately you would have to go to jisho.org which would defeat the purpose of a pop-up dictionary where you can get the meaning without going to a dictionary website.

Would there be a way to find out which is the correct pronunciation without going to a dictionary website?

 

[Majestic]

Years of practice. There is no other way to know (intuitively or objectively) which choice is most appropriate, because the reading depends on the situation.

 

[Toritoribe]

Would there be a way to find out which is the correct pronunciation without going to a dictionary website?

As far as I know, no. It's possible just to show which reading is more frequently used, but the most common reading is not always the correct reading. As you can see in the examples like 左腕 or 右腕, it's necessary to know the context to identify the correct reading, and I don't think it's possible to show these kinds of detailed information concisely in a pop-up window.

 

[panlanc]

Is it possible to show the more frequently used one 1st and then lesser one 2nd?

 

[panlanc]

It used to be that there was a similar pop-up dictionary in Firefox called Perapera-kun (both Japanese and Chinese version). In my experience it was superior to Rikai kun of Chrome, because it always showed the most commonly used pronunciation at the top, and the less common one below that.

But at a certain point the developer stopped developing it, so that if you updated your Firefox at a certain point, you could no longer use them.
But overtime, someone brought over the Chinese version of Peraperakun so that now it's compatible with newer versions of Firefox, with the permission of the original developer. But the Japanese Peraperakun is still missing.

 

[Toritoribe]

"The order of frequency" doesn't solve your problem, since the most common reading is not always the correct reading, as we already pointed out.