Answer:

Step-by-step explanation:

The first number 1.23 is CALLED the coefficient. It must be greater than or equal to 1 and less than 10.

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