Express the given decimal as a fraction. $1.441441441 \ldots$
A) $\frac { 160 } { 111 }$
B) $\frac { 174 } { 143 }$
C) $\frac { 49 } { 111 }$
D) $\frac { 60 } { 11 }$

Question

Quizplus · Accepted Answer

To express the repeating decimal $1.441441441 \ldots$ as a fraction, let $x = 1.441441441 \ldots$. Multiplying both sides by 1000 (to shift the decimal three places to the right) gives $1000x = 1441.441441441 \ldots$. Subtracting the original equation from this, $999x = 1440$, simplifies to $x = \frac{1440}{999} = \frac{160}{111}$.

Express the Given Decimal as a Fraction 1.441441441…1.441441441 \ldots1.441441441… A) 160111\frac { 160 } { 111 }111160​

Express the Given Decimal as a Fraction $1.441441441 \ldots$ A) $\frac { 160 } { 111 }$