Scientific Notation

Scientific notation is a method for expressing very large or very small numbers in powers of 10.  Scientific notation will make your life easier because of its short hand method for writing numbers and its easy method for calculations.  Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent.

  Ex. 1:                                         6.03 x 10⁷ exponent
                                                  coefficient         base

1. The coefficient must be greater than or equal to 1 and less than 10.
2. The base must be 10.
3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.  A negative exponent means that the decimal is moved to the left when changing to standard notation.

Solution: Simply move the decimal seven places to the right because the exponent is 7.

 Ex. 2: Change 5.3 x 10^-4 to standard notation.

So, 6.03 x 10⁷ = 60 300 000

The exponent tells us to move the decimal four places to the left.

so, 5.3 x 10^-4 = 0.00053

If calculating scientific notation on a calculator, the numbers in scientific notation must be entered in E notation.

For example, 1.23 x 10^7 is entered as 1.23E7 or 1.23e7.

Example of Unitary Rates
  

1m = 100cm

1m² = 100cm²  (100cm X 100cm)

1m³ = 100cm³  (100cm X 100cm X 100cm)

 

1Mg = 1,000,000g

1Mg² = 1,000,000g²  (1,000,000g X 1,000,000g)

1Mg³ = 1,000,000g³  (1,000,000g X 1,000,000g X 1,000,000g)

 

 

Convert: 72dam² into mm²

 

dam → mm

1dam → 10⁴mm

1dam² → 10^4X2mm²

1dam² → 10⁸mm²

 

72dam² X 10⁸mm²  = 72 X 10⁸mm²

                 1dam²

 

= 7.2 X 10⁹mm²

 

 

By: Hikari Hoshika  &  Jason Zhang