Simplify the following
(a) (2.2 x 10') x (1 x 1014)
Answers
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