Zero (0) and one (1) are very special numbers. They possess the important properties given below:
Addition property of zero
Adding 0 to a number leaves its same. 0 is called the additive identity and the property is called the additive identity property.
4 + 0 = 4
0 + 3 = 3
Multiplication property of zero
Zero times any number is equal to zero. Which means, multiplying any number by 0 gives 0.
0 × 7 = 0
2 × 0 = 0
Multiplication property of one
Multiplying any number by 1 leaves it unchanged. 1 is called the multiplicative identity hence the property is called multiplicative identity.
1 × 36 = 36
23 × 1 = 23
Exponents of one
The number one raised to any power is always one.
1100 =1
1-34 =1
Exponent one
Any number raised to power one remains unchanged.
31 = 3
-51 = -5
Exponents of zero
The number zero raised to any power is remains zero.
024 = 0
0-9 = 0
Exponent zero
Any number raised to power zero is one
450 = 1
-230 = 1
Zero as numerator
Zero divided by any non-zero number is zero.
0 ÷ 3 = 0
0 ÷ 6 = 0
Zero as denominator
Any division by zero is not defined
9 ÷ 0 = not defined
3 ÷ 0 = not defined
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