decreasing slightly in value over the year he was in office.

In contrast to the blue-blooded Mr. Aso and Mr. Abe–both are multigenerational parliamentarians with grandparents who served as prime ministers–records showed that Mr. Noda, known as the pauper premier, left his premiership a tad bit poorer, with just ¥16.3 million to his name–his house in Chiba Prefecture decreasing slightly in value over the year he was in office.

What does the bold part suggest here?

It means that the value of his house decreased slightly during the year he was in office. “the year he was in office” means the year that he was premier.

(¥16.3 million, being only about £110,000, does seem an amazingly low amount for the total wealth of a former Japanese prime minister. I wonder if that really is accurate!)

I think it’s accurate. I got it from a reliable source.

Does 16.3 million worth properties include his house in Chiba?

The implication is that it does.

Thanks, Dozy, I understand now.

Another:
Rahim had in more than 60 years of public life reigned as king, governed as head of state and prime minister, and jostled for power from exile.

What does the bold part suggest? Does it suggest that “Rahim” was exiled from power?

It means that he was exiled from the country (expelled or fled, and not able to return).

Could you please give me an alternative way to express the bold part?

He was exiled from his country (expelled or fled, and not able to return). While he was in exile, he jostled for power (vied to gain some kind of political power).

Yes, Dozy, I understand now. Your explanation is very helpful.

Thanks for your swift replay.