LESSON: Exponential Notation

Exponential Notation

In the definition of physics, it was noted that physics deals with objects as small as sub-atomic particles and as large as galaxies.  It should be clear that physicists deal with extremely small numbers like the mass of a lead atom, 0.00000000000000000000034 gram, and extremely large numbers like the distance from our galaxy to the Andromeda galaxy, 2.5 million light years, which is 25,000,000,000,000,000,000 kilometers.

These numbers are difficult to write and even more difficult when calculations must be done.  It is much more convenient to write and calculate with such extreme numbers if they are written in exponential form.  In exponential form, the mass of a lead atom is 3.4 × 10-34 g, and the distance from our galaxy to the Andromeda galaxy is 2.5 × 1019 km.

A number is expressed in exponential form by moving the decimal so that exactly one non-zero digit is on the left of the decimal and the exponent of 10 will be the number of places the decimal was moved.  If the decimal is moved to the left, the exponent is positive and if the decimal was moved to the right, the exponent is negative.  All significant figures are maintained in exponential notation.

Example: Express 13,700,000,000 in exponential form.

Solution: Since the decimal will be moved to the left 10 places, the exponent will be 10.  So, the correct exponential form is 1.37 × 1010.

Example:  Express 0.000000000000000074 in exponential form.

Solution:  Since the decimal will be moved to the right 17 places, the exponent will be -17.  So the correct exponential form is 7.4 × 10-17.

Example:  Express the number 8.43 × 105 in expanded form.

Solution:  105 is 100,000 so 8.43 × 105 is 8.43 × 100,000 or 843,000.

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