Is a 3.0 GHz single core processor much slower than a 3.0 GHz dual core?

It's not only the clock frequency of the individual cores but the efficiency of those cores.

Looking at the mid-generation pentium4 CPU's which at the time were well regarded

(but have been superceeded by better, newer CPU families)

the Pentium-M CPU's (the "Parent" of the "core" family) would out perform

Pentium4 CPU's running at 50% greater clock speed.

I know personally that a PentiumM 740 1.73GHZ CPU stomps all over most 2.8GHz Pentium4's

while using a maximum of 1/3 of the power!

The "Core family" which is based on PentiumM technology greatly increases the number of transistors on the die and they generally have even more L2 Cache

The real thing about the Pentium4 is that they needed all that clockspeed to make up for other inefficiencies in their design.

So once again there is far more than "clock speed"

My current Quad-Core Desktop (a two year old Q9450 CPU)

had FOUR TIMES the number of transistors inside the CPU as

the TOTAL number of transistors in my last Dual core computer

and three times the L2 Cache.

Not only does it convert a 15Mb *.flv file to an *.mp4 video file in about 40seconds

it wil convert THREE OF THEM simultaneously...

My old dual core computer took 8minutes to convert ONE file at a time.

Generally speaking it will cost you less to buy a newer faster computer than

upgrade your three generation old computer.

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Pentium 4's are slow... very slow. You can buy a hundred dollar quad core processor (AMD Athlon 2 x4) nowadays that will easily whoop the Pentium 4 and Pentium D series.

In terms of performance even a year 2007 Core 2 Duo clocked at 2.4 ghz will easily beat a 3.4ghz Pentium 4. The clock speed of the processor means nothing. Even though the clock speed is at 3ghz, the Pentium 4 uses very old technology and has far less transistors on it's processor die compared to a CPU that was made this year.

A dual core 3.0 is 50% faster than a single core 3.0. Theoretically, anyway.

for minecraft yes... it would improve performance .however upgrading to a dual core cpu would be very helpful for other computing tasks... also for improved minecraft experience a nicer video card can really help.