Find the rational number representation of the repeating decimal.
$0 . \overline { 167 }$
A) $\frac { 167 } { 9999 }$

B) $\frac { 16.7 } { 999 }$

C) $\frac { 167 } { 9 }$

D) $\frac { 167 } { 999 }$

E) $\frac { 167 } { 99 }$

Question

Find the rational number representation of the repeating decimal.
$0 . \overline { 167 }$
A) $\frac { 167 } { 9999 }$

B) $\frac { 16.7 } { 999 }$

C) $\frac { 167 } { 9 }$

D) $\frac { 167 } { 999 }$

E) $\frac { 167 } { 99 }$

Quizplus · Accepted Answer

The repeating decimal $0.\overline{167}$ can be converted into a fraction by recognizing that the repeating part (167) is over a denominator that has the same number of 9s as there are digits in the repeating sequence. Since "167" has three digits, the denominator should have three 9s, making the fraction $\frac{167}{999}$.

Find the Rational Number Representation of the Repeating Decimal 0.167‾0 . \overline { 167 }0.167

Find the Rational Number Representation of the Repeating Decimal $0 . \overline { 167 }$