The concept behind exponential notation is to express
numbers using powers of 10

a × 10^{b} (1)

where a is a real number and the exponent , b is an integer. The number a is
written in such a way that

it is greater than 1 but less than 10. To find the value of b

1. For numbers > 1, count right to left the number of digitst up to but not
including the leftmost

one. Example:

123, 400, 000 = 1.234 × 10^{8} (2)

2. For numbers < 1, count from the decimal point to just past the first non-zero
digit; b is a negative

number. Example:

0.0001234 = 1.234 × 10^{-4} (3)

Multiplication and Division are performed by multiplying the real numbers
together then either

adding or subtracting the exponents . If the resulting real number is larger than
10 or smaller than 1,

the final exponent must be adjusted. Given

then

To raise a number in scientific notation to some
exponential power n (e.g. squaring a number ),

again raise the real number a to the power, then multiply the exponent by the
power. For Example:

Some Examples:

1. Multiply 2.5×10^{4} by 12.2×10^{2}. This equals 30.5×10^{6}, but the first real number
should not be

bigger than 1, so this would be written as 3.05×10^{7}

2. Square the distance between the Earth and sun (1.495×10^{8} km). This
is equivalent to (1.495)^{2}

× 10^{8+8} = 2.235025 × 10^{16}.

3. Divide the mass of an electron (9.1093826×10^{-31}) by 100. This results in:
9.1093826×10^{-33}.