Give the sum p+q where p/q is the reduced fraction represented by the repeating decimal 1.36
Choices
a. 13
b. 19
c. 26
d. 28
Hello, ccdalamp!
Here's an algebraic solution . . .Give the sum $\displaystyle p+q$ where $\displaystyle \frac{p}{q}$ is the reduced fraction
represented by the repeating decimal $\displaystyle 1.\overline{36}$
Choices: . $\displaystyle a)\;13\qquad b)\;19 \qquad c)\;26\qquad d)\; 28$
Let $\displaystyle N \:=\:1.363636...$
Multiply 100: .$\displaystyle 100N \;=\;136.363636...$
. Subtract $\displaystyle N\!:\quad\;\;\;N \;=\quad\; 1.363636...$
And we have:. $\displaystyle 99N \;=\;135\quad\Rightarrow\quad N \:=\:\frac{135}{99} \:=\:\frac{15}{11}$
Therefore: .$\displaystyle p + q\:=\:15 + 11\:=\:26$