Scientific Notation and Standard Form

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 ×10 6 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 ×10 6 , the mantissa is the "1"

• 1.2 ×10 14 the positive exponent indicates a large number
• 4.22×10 11
• 7.89 × 10 -21 the negative exponent indicates a small number

• Scientific Notation Worksheets (free pdfs with answer keys on scientific notation)

• scientific notation in action
• Problem Set #2

General Formula of Scientific Notation

The general from of a number in scientific notation is:

a ×10 n 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 ×10 4 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 which is "a" in this example, is smaller than 1 which is not allowed in scientific notation

• 10's exponent is not an integer.

• 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

Practice Problems

In the following sentences, convert from scientific notation to standard form.

In the following sentences, convert from standard form to scientific notation.

In the following sentences, state whether or not the given number is in Scientific Notation and explain your answer.