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Exponential Notation Tutorial

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

× 10b  (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 × 108  (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


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 2.5×104 by 12.2×102. This equals 30.5×106, but the first real number should not be
bigger than 1, so this would be written as 3.05×107

2. Square the distance between the Earth and sun (1.495×108 km). This is equivalent to (1.495)2
× 108+8 = 2.235025 × 1016.

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

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