what is the meaning of いくわけだ

Question

From a passage saying that it's hard for people to visualize or grasp the scale of things when they're in expressed in units they can't easily relate to- but that if something people can relate to is used people can get an idea more easily. The sentence I'm unsure about is:

例えば、「東京ドーム５。７杯分」と書けば、「ああ、そんなに多いのか」と納得がいくわけだ。

'For example. if it's written that Tokyo Dome is the equivalent of 5.7 glasses(??), then people can get an idea of the scale, thinking 'ooh its that big is it'. - Is my understanding of that.

I understand 'wake' and 'iku' seperately as reasoning, and go respectively. However, when they're together here, does it basically mean, 'goes the reasoning'? Or is there a different nuance going on here?

Answer 1

～は納得が行く is a set phrase that means:

1. ～ makes sense; ～ sounds convincing; one is satisfied by ～

   その説明は納得が行きません。もっと詳しく話してください。
   納得の行く説明が欲しい。

2. ～ is satisfied (by an explanation); ～ is convinced (by something)

   彼はまだ納得が行かないようだ。
   あなたが納得が行くまで、何度でも教えます。

This usage of 行く is described as the tenth definition of this entry, but practically you'll have to memorize this rather than analyze this.

訳【わけ】 means reason. ～わけだ means "it's natural to think ～", "no wonder ～", "therefore ～", "as a natural consequence, ～", etc.

「ああ、そんなに多いのか」と納得がいくわけだ。
(saying it) will naturally make sense to you — "Ah, it's that much!"