Its the additive identity prosulate
The correct answer is 1.7 times 10^3.
Step-by-step explanation:
Step 1:
Let x equal the repeating decimal you are trying to convert to a fraction.
Step 2:
Examine the repeating decimal to find the repeating digit(s).
Step 3:
Place the repeating digit(s) to the left of the decimal point.
Step 4:
Place the repeating digit(s) to the right of the decimal point.
Step 5:
Using the two equations you found in step 3 and step 4, subtract the left sides of the two equations. Then, subtract the right sides of the two equations
As you subtract, just make sure that the difference is positive for both sides.
Set the whole expression = to 0 and solve for x.
3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0
Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.
In the latter case, 4x^(2/3) = 3.
To solve this: mult. both sides by x^(-2/3). Then we have
4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as
4 3
--- = --------------------
1 x^(+2/3)
Then
4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)
Check this result! subst. 0.65 for x in the given equation. Is the equation then true?
My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?
