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TeddyBonham
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Sat Mar 28, 2015 2:21 am
In the identity above, x+y and x-y are called CONJUGATES.
It is possible to rephrase decimals as follows:
1.01 = 1 + .01.
.99 = 1 - .01.
Notice that (1 + .01) and (1 - .01) are CONJUGATES:
= (1 + .01)(1 - .01)
= 1² - (.01)²
= 1 - .0001
= .9999.
Notice also that the product of these conjugates (.9999) looks VERY SIMILAR to the denominators in the problem below. .
The two DENOMINATORS in the problem above can be rephrased as follows:TeddyBonham wrote:0.999991/0.997 - 0.999996/0.998 = ?
1. 10^-6
2. 3*10^-6
3. 10^-3
4. 2*10^-3
5. 3*10^-3
.997 = 1 - .003
.998 = 1 - .002.
In order for these two denominators to CANCEL OUT, the two NUMERATORS must be composed of the following sets of CONJUGATES:
(1 + .003)(1 - .003)
(1 + .002)(1 - .002).
Thus:
0.999991/0.997 - 0.999996/0.998
= [(1 + .003)(1 - .003) / (1 - .003)] - [(1 + .002)(1 - .002) / (1 - .002)]
= (1 + .003) - (1 + .002)
= .001
= 10^(-3).
The correct answer is C.
