Part
1: How Do we Multiply numbers in Scientific Notation?
Scientific Notation is based
on powers of the base number 10.
The number 123,000,000,000 in scientific notation is written as :
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 10^{11} 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 10^{4})(2x 10^{5}) = 6 x 10^{9}
What happens if the coefficient
is more than 10? Example
2: (5 x 10 ^{3}) (6x 10^{3}) = 30. x 10^{6 }
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.x10^{6}
= 3.0 x 10^{7}^{ }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 10^{4})(5 x
10^{6})(3 x 10^{2}) = 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 10^{8}) = 6. x 10^{-5} 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). Go
to Division in Scientific Notation |