sampling rate Matlab
You reasoning is NOT correct. One period is 10 samples long, not 11. The 11th sample is the first sample of the 2nd period, not the last sample of the 1st period.

So originally you have


sample rate: 10 MHz
sine wave frequency: 1 MHz, which is 1/10th of the sample rate


If you want to get a 1 kHz sine wave you need to set the sample rate to 10 times 1 kHz, i.e. 10 kHz. If you play it back at a sample rate of 909 Hz, your resulting frequency would be 90.9 Hz.