Is it worth buying the JR Pass?

Hi

I am traveling to Japan next July and here is my itinerary so as to tell me if it's worth buying JR pass for 7 days.

Day 1: Arrival to Tokyo, Tokyo
Day 2: Tokyo
Day 3: Day trip to Mt Fuji
Day 4: Day trip to Nikko
Day 5: Tokyo
Day 6: Tokyo - Nagoya (sumo tournament) - Osaka
Day 7: Osaka - Kyoto - Osaka
Day 8: Osaka - Nara - Osaka
Day 9: Osaka - Hiroshima - Miyajima - Osaka
Day 10: Osaka - airport departure

the plan is to start using the pass from Day 3.

If I first use the pass in the morning of Day 3 does it expire on the evening of Day 9 or in the morning of Day 10 (same time used in Day 3)

What do you think? Is it worth buying the JR Pass 7 Days?

Thanks
George

Yes.

the plan is to start using the pass from Day 3.

What do you mean by "Mt Fuji"? Kawaguchiko or Hakone?

What time do you have to be at Kansai Airport on Day 10? What else do you plan on doing on Day 10? Where is your hotel located on the night of Day 9?

It may be more economical to start your JR Pass on Day 4 so that it covers you from Osaka to Kansai Airport, plus whatever else you do that day.

If I first use the pass in the morning of Day 3 does it expire on the evening of Day 9 or in the morning of Day 10 (same time used in Day 3)

Almost all passes in Japan work on calendar days and don't care what time you activate them. So, it expires in the evening of Day 9 no matter what time you activate it on Day 3.

What do you think? Is it worth buying the JR Pass 7 Days?

As shen said, yes.

Enjoy your trip!