Yes a L=1000ml (a L is 1000 bigger than a ml!)
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No. It is one tenth the size.
Milliliters are smaller than cups.
No. They are exactly the same.
A liter is the metric base unit for volume. The prefix "milli-," in this case, means "one-thousandth." So a milliliter is one-thousandth of a liter. Therefore, a liter is bigger.
1 liter has 1,000 milliliters in it, so it's probably somewhat bigger than each milliliter.