Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as :

The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10¹¹ the number 11 is referred to as the exponent or power of ten.

Rules for Multiplication in Scientific Notation:

1) Multiply the coefficients

2) Add the exponents (base 10 remains)

Example 1: (3 x 10⁴)(2x 10⁵) = 6 x 10⁹

What happens if the coefficient is more than 10 when using scientific notation?

Example 2: (5 x 10 ³) (6x 10³) = 30. x 10⁶

While the value is correct it is not correctly written in scientific notation, since the coefficient is not between 1 and 10. We then must move the decimal point over to the left until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be raised 1 power of ten.

30.x10⁶ = 3.0 x 10⁷ in scientific notation.

Example 3:

(2.2 x 10 ⁴)(7.1x 10 ⁵) = 15.62 x 10 ⁹ = 1.562 x 10 ¹⁰

Example 4:

(7 x 10⁴)(5 x 10⁶)(3 x 10²) = 105. x 10 ¹² --now the decimal must be moved two places over and the exponent is raised by 2. Therefore the value in scientific notation is: 1.05 x 10 ¹⁴

Now Try these:

(write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 ³ you should type 3.5x10^3 in the box then click the submit button).

What happens when the exponent(s) are negative?

We still add the exponents, but use the rules of addition of signed numbers.

Example 5: (3 x 10 ^-3) (3x 10^-3) = 9. x 10^-6

Example 6: (2 x 10 ^-3) (3x 10⁸) = 6. x 10⁵

Now Try these:

(write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 ³ you should type 3.5x10^3 in the box then click the submit button). Multiply the following:

Go to Division in Scientific Notation