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

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) (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.
RELATED QUESTIONS
Create an equation of a nonlinear function and provide two inputs for your classmates to... (answered by solver91311)

Please help me solve the problem. Thank you! f(x)=x+4 f(-8) f(-4) Non-linear... (answered by RAY100)

Domain D = {5, 2, -4} F (X) = X2 to the second power + 3x + 1 Evaluate the equation (answered by stanbon)

please help me solve... xy = -13 and y = 7/x both with inputs of 0 and... (answered by Fombitz)

Complete the equations of the system in slope-intercept form. Use a decimal for the slope (answered by Alan3354)

A linear system may have a unique solution, no solution, or infinitely many solutions.... (answered by MathLover1)

determine a and b for which the system of linear equation has infinite no. of solutions:... (answered by mananth,Theo)

Find a value of n so the linear system has an infinite number of solutions x-y=4... (answered by stanbon)

Which equation would make this system have an infinite number of solutions? {y=x+2... (answered by rwm)