Question

Determine which number is in "proper" scientific notation.

Answer 1

The number 2.31 * 10⁻⁴ is a proper scientific notation.

The simplified expression of
`((1)/(c) + (1)/(d))/((c)/(d) - (d)/(c))` is (c)
`(1)/(c - d)`

Determining which number is in proper scientific notation.

From the question, we have the following parameters that can be used in our computation:

The list of options

By definition

Numbers in their scientific notation are represented using

a * 10ⁿ

Where

a is a real number between 1 and 10

And n is an integer

Using the above as a guide, we have the following:

2.31 * 10⁻⁴ is a proper scientific notation.

How to simplify the expression

Here, we have

`((1)/(c) + (1)/(d))/((c)/(d) - (d)/(c))`

Take the LCM of the fractions

`((1)/(c) + (1)/(d))/((c)/(d) - (d)/(c)) = ((d + c)/(cd) )/((c^2 - d^2)/(cd))`

Evaluate the quotient

`((1)/(c) + (1)/(d))/((c)/(d) - (d)/(c)) = (d + c)/(c^2 - d^2)`

Apply the difference of two squares

`((1)/(c) + (1)/(d))/((c)/(d) - (d)/(c)) = (d + c)/((c - d)(c + d))`

So, we have

`((1)/(c) + (1)/(d))/((c)/(d) - (d)/(c)) = (1)/(c - d)`

Hence, the simplified expression is (c) 1/(c - d)