Why is any number multiplied by zero zero

Dave Donaghy, Bath ddonahey mltsa. The fact that it can be related to the real world is fortuitous and convenient. However it is far from always the case. Pi is a number in any proper sense as too is e - the number I talk about below.

These numbers have an interesting property, amongst others - it is impossible to write them down, unless you accept some error, because they contain an infinite "number" of digits.

Hence in any "real" experiment one will always get into the mess which Jack Belck describes above. This might sound pedantic but leads to some important consequences.

Try it out with a piece of graph paper and a pocket calculator, or do the Taylor expansion of exp x. Dr Simon Evans, London s. They do not apply to any number system of any use, as explained by previous answers.

His second hypothesis gives zero divided by zero equals one and the third gives zero divided by zero equals infinity. From this we can immediately conclude that in any number system satisfying his hypotheses, infinity is equal to one. If we additionally assume that "zero divided by zero" means "the unique number which gives zero when muliplied by zero", we see that zero is also equal to the common value of one and infinity, and to any other numbers that may exist in the system under consideration.

To sum up: under the conditions given, every number is equal to the same value, call it zero, one, infinity or whatever you like. We have no more boxes, so we have no lots of We say that zero lots of any number always equals zero. It does not matter what the number is, if it is multiplied by zero, then the answer is zero.

In this example we have 3 empty boxes. Each box contains zero eggs so in three boxes we say we have 3 lots of 0. Even if we add another empty box, we are not adding any eggs. We still have zero in total. It does not matter how much of nothing you have, it is still nothing.

Here are some examples of multiplying by zero. Remember that it does not matter what the other numbers are, as long as we are multiplying by zero, then the answer is zero. It total we have nothing. It does not matter how large the other number is, 57 lots of nothing is still nothing. This is like having 57 empty boxes of eggs.

There are still no eggs in any of them. Even if there are many numbers multiplied together, the answer is still zero if we are multiplying by zero. There are still no eggs in total because all of the boxes are empty. How to Multiply by 1 The rule for multiplying any number by 1 is that the number remains the same size. When multiplying a given number by one, the answer is simply the given number.

To understand why this rule works we will look at some examples of multiplication. Here is a single box of 10 eggs. It is just one box so we say we have one lot of ten. Here is a box of 6 eggs. We can see in both of these cases, the answer shown after the equals sign is simply the other number that is multiplied by 1. We say that a given number multiplied by one equals the given number.

Even mathematicians often struggle to explain why dividing by zero doesn't work. The reason is essentially related to the multiplication property. The concept of dividing by zero is fraught with illogical consequences, so much so that its mythical destructive power has become a joke on the Internet.

There is also the property of the zero exponent; because of the existence of negative exponents, numbers to the negative power, numbers to the zero power always equal one. Although this works mathematically, it too presents logical problems. Chiefly, zero to the zero power still equals one, although zero added or subtracted to or multiplied by itself should equal zero [source: Stapel ]. Sign up for our Newsletter! Mobile Newsletter banner close.

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