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Multiplying by Zero

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Multiplying by Zero, a selection of answers from the Dr. Math archives.

Multiplying by 0
Why, when multiplying any number by 0, do you get 0?

Zero and the Commutative Property of Multiplication
If we take 0x1, we get 0, and if we take 0x2, we still get 0, for it is still 0+0+0. But if we do it the other way round, why must it still be 0, if any number to the power of 0 = 1?

Multiplying by Zero
Why does any number times zero equal zero?

Multiplying by Zero
I know that zero's value is nothing, but why is it that it turns other numbers that clearly have a greater value to zero when multiplied?

Paradox in the Zero Power
Why does the product of multiplying a number by itself zero times equal 1?

And see the Dr. Math FAQ:

0 to 0 power
What is 0 to the 0 power?

0! = 1
Why does 0! = 1?

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