Part
2: How Do we Divide 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 Division
in Scientific Notation: 1)
Divide the coefficients 2)
Subtract the exponents (base 10 remains) Example
1: (6 x 10^{6}) / (2 x 10^{3}) = 3 x 10^{3}
What happens if the coefficient
is less than 10? Example
2: (2 x 10 ^{7}) / (8 x 10^{3}) = 0.25 x 10^{4}
While the value
is correct it is not correctly written in scientific notation since the
coefficient is not between 1 and 10. We must move the decimal point over to the
right until the coefficient is between 1 and 10. For each place we move the decimal
over the exponent will be lowered 1 power of ten. 0.25x10^{
4} = 2.5 x 10^{3}^{ }in scientific notation.
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 subtract the exponents (apply the rules for subtracting signed numbers) Example
5: (9 x 10 ^{-6}) / (3x 10^{-3}) = 3. x 10^{-3} Example
6: (2 x 10 ^{3}) / (4 x 10^{-8}) = 0.5 x 10^{11 }= 5 x
10^{ 10} 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 Word Problems Using Scientific Notation |