What is pi? (1000 iterations.) <-- This is accurate to 3 significant figures
What is pi? (10000 iterations.) <-- This is accurate to 4 significant figures
What is pi? (100000 iterations.) <-- This is accurate to 5 significant figures
What is pi? (1000000 iterations.) <-- This is accurate to 6 significant figures

What is e? (10 iterations) <-- This is accurate to 6 significant figures
What is e? (20 iterations) <-- This is accurate to 16 significant figures
What is e? (50 iterations) <-- This is accurate to greater than 16 significant figures
What is e? (100 iterations) <-- This is accurate to greater than 16 significant figures

What is e? (k=1,000,000) <-- This is accurate to 6 significant figures
What is e? (k=2,000,000) <-- This is accurate to 7 significant figures
What is e? (k=5,000,000) <-- This is accurate to 7 significant figures
What is e? (k=10,000,000) <-- This is accurate to 9 significant figures
What is e? (k=100,000,000) <-- This is accurate to 8 significant figures
What is e? (k=1,000,000,000) <-- This is accurate to 7 significant figures

Computers don't tend to be very good at floating point numbers as they cannot be fully expressed as a binary number, therefore the number of significant figures that the answer is accurate to starts to drop off when the numbers get bigger.