SOLUTION: 1. x=1.9285714285714285714..... y=0.3333333333333333333...... Evaluate x+y 2. A system with two inputs of periodic infinite decimal numbers is designed such that,it perfor

Algebra ->  Decimal-numbers -> SOLUTION: 1. x=1.9285714285714285714..... y=0.3333333333333333333...... Evaluate x+y 2. A system with two inputs of periodic infinite decimal numbers is designed such that,it perfor      Log On


   

Question 344951: 1. x=1.9285714285714285714.....
y=0.3333333333333333333......
Evaluate x+y
2. A system with two inputs of periodic infinite decimal numbers is designed such that,it performs addition between two inputs and gives single output. Would the output be a periodic decimal number? Discuss the answer using mathematical analysis of the situation.
3. If you are required to use such a single system and form a 6 input:1 output
system will you be able to guarantee that the output would be same as you discussed in be?
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
1. x=1.9285714285714285714.....
y=0.3333333333333333333......
Evaluate x+y

Either we notice that 428571 is typical of seventh fraction : x=10/7+0.5

x+y=1/3+10/7+1/2=(14+60+21)/42=95/42


or by using : 0.a1a2a3...an(periodic)=a1a2a3...an/99...9 denominator : n 9's))

y=3/9=1/3, x=1.9+0.0285714...=19/10+1/10*285714/999999

x+y=1/3+19/10+285714/9999990=(3333330+19*999999+285714)/9999990
=(3619044+19000000-19)/9999990=(22619044-19)/9999990=22619025/9999990 (simpl 5)

=4523805/1999998 (simpl 3)=1507935/666666(simpl 3) =502645/222222(simpl 11)

=45695/20202(simpl 13)=3515/1554(simpl 37)=95/42


2. and 3. since a periodic decimal number can be written in form of a fraction with the formula above, the sum of periodic decimal number will be a fraction again, which is a periodic decimal number.