Scientific notation is just a short hand way of expressing gigantic numbers like 1,300,000 or incredibly small numbers like 0.0000000000045. Also known as exponential form, scientific notation has been one of the oldest mathematical approaches. It is favored by many practicioners. If numbers are too big or too small to be simply calculated, people reffer to scientific notation to handle these circumstances. This method is used by engineers, mathematicians, scientists.
An example of scientific notation is 1.3
×106
which is just a different way of expressing the standard notation of the number 1,300,000. Standard notation is the normal way of writing numbers.
Key Vocabulary
- mantissa = this is the integer or first digit in any Scientific Notation. For example in 1.3 ×106, the mantissa is the "1"
General Formula of Scientific Notation
The general from of a number in scientific notation is
a ×10n where 1 ≤ a ≤ 10 and n is an
integer. In other words the number that we'll call "a" is is multiplied by 10, raised to some exponent n. This number "a" must be no smaller than 1 and no larger than 10. To illustrate this definition examine the following:
1.4 ×104 is a
proper example of scientific notation because
1.4, which is "a" in this example, is not smaller than 1 and not larger than 10 so it's ok.
10's exponent is the integer 4.
.9 ×104 is a NOT
proper example because
.9 which is "a" in this example, is smaller than 1 which is not allowed in scientific notation
3.34 ×10½ is a NOT
proper example because
10's exponent is not an integer.
4.34 ×10-55 is a proper example because
4.34, which is "a" in this example, is not smaller than 1 and not larger than 10
10's exponent is the integer -55. Integers can be negative
In the following sentences, convert from standard form to scientific notation.
the positive exponent indicates a large number 
Scientific Notation Worksheets (free pdfs with answer keys on scientific notation)