When it comes to cutting a kilogram of pure gold, you can continue to halve the portion until you reach a size that cannot be practically divided. Initially, you have a whole kilogram, which is equivalent to 1,000 grams.
When you cut the gold in half, you will keep halving the weight:
- 1st cut: 1000 grams becomes 500 grams
- 2nd cut: 500 grams becomes 250 grams
- 3rd cut: 250 grams becomes 125 grams
- 4th cut: 125 grams becomes 62.5 grams
- 5th cut: 62.5 grams becomes 31.25 grams
- 6th cut: 31.25 grams becomes 15.625 grams
- 7th cut: 15.625 grams becomes 7.8125 grams
- 8th cut: 7.8125 grams becomes 3.90625 grams
- 9th cut: 3.90625 grams becomes 1.953125 grams
- 10th cut: 1.953125 grams becomes 0.9765625 grams
After making 10 cuts, you have a piece of gold that weighs less than a gram, which can still be handled or divided further, making it challenging to split in practical terms. However, theoretically, if you keep going, you’ll eventually end up with particles that are far too small to be considered a substantial piece of gold.
It is important to also consider the limits of physical manipulation; once you reach sizes around 0.1 grams or even smaller, the gold may not be effectively cut without specialized equipment, and you would also encounter issues at the atomic level. Thus, while you could keep dividing theoretically, you’d reach a point where cutting isn’t practical.
In conclusion, although you can continue to cut a kilogram of pure gold many times, practical limitations would suggest that cutting it more than 10 to 12 times puts you at a size where further division becomes increasingly impractical.