The phrase "10 times smaller" is grammatically nonsensical, or more accurately, it doesn't really mean what people think it means. 10 times a centimeter is 10 centimeters, so to be 10 times smaller than 1 centimeter would be -9 centimeters 1cm - (10 x 1cm) = -9 centimeters.
The more correct way to ask the question is (at least, this is what people usually mean when they say "X times smaller"), "What distance is 1/10th the size of a centimeter?" To which the answer is 1 millimeter.
1 centimeter is 1/100th of a meter (1 cent of a meter).
1 millimeter is 1/1000th of a meter.
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A centimeter (cm) is 100,000 times smaller than a kilometer (km).
A centimeter is smaller than a meter
A decimeter is ten times smaller than a meter
No, its bigger.