The concept behind exponential notation is to ex press
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 exp onent 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}.