[guanaco]

The paragraph starting "when they say..." is wrong. If the old device runs at 100 MHz and the new device runs at 130 MHz, the speed-up is described indeed as 30% faster. But translated to decimals, 30% faster is not 0.30, it is 1.30. Why? the answer is because 100 * 1.30 = 130.

The speed-up formula is S = new / old. Thus, in the example above, S = 130 / 100 = 1.30, that is 30% faster.

100% faster is not 1.0 faster, is 2.0 faster. For example, if old device runs at 100 MHz and new device is 200 MHz, then S = 200 / 100 = 2.0, that is 100% faster.

2X faster means the new device is 2 times faster, that is 100% faster.

1X faster means the 2 devices have the same speed. For example, if both devices runs at 100 MHz, then S = 100 / 100 = 1.

If all these sounds exotic, please see the section 1.6 of "Computer Organization and Design" by Patterson and Hennessy. There is a nice discussion about performance and how to measure it.