Lesson
Notes
| \({\text{Examples of Repeating Decimals}}\) |
| \(\underline{\text{Decimal}}\) |
\(\underline{\text{Fraction}}\) |
| \(0.\overline{5}\) |
\(\frac{5}{9}\) |
| \(0.\overline{54}\) |
\(\frac{54}{99}\) |
| \(0.\overline{541}\) |
\(\frac{541}{999}\) |
| \(0.\overline{5415}\) |
\(\frac{5415}{9999}\) |
Practice Problems
Express the following repeating decimals as fractions.
\(\textbf{1)}\) \(\hspace{1ex}0.\overline{4}\)
The answer is \(\frac{4}{9}\)
\(\textbf{2)}\) \(\hspace{1ex}0.\overline{6}\)
The answer is \(\frac{2}{3}\)
\(\textbf{3)}\) \(\hspace{1ex}0.\overline{45}\)
The answer is \(\frac{45}{99}=\frac{5}{11}\)
\(\textbf{4)}\) \(\hspace{1ex}0.\overline{457}\)
The answer is \(\frac{457}{999}\)
\(\textbf{5)}\) \(\hspace{1ex}0.\overline{36}\)
The answer is \(\frac{36}{99}=\frac{4}{11}\)
\(\textbf{6)}\) \(\hspace{1ex}0.\overline{87}\)
The answer is \(\frac{87}{99}\)
Express the following fractions as repeating decimals.
\(\textbf{7)}\) \(\hspace{1ex}\frac{7}{9}\)
The answer is \(0.\overline{7}\)
\(\textbf{8)}\) \(\hspace{1ex}\frac{67}{99}\)
The answer is \(0.\overline{67}\)
\(\textbf{9)}\) \(\hspace{1ex}\frac{1}{3}\)
The answer is \(0.\overline{3}\)
\(\textbf{10)}\) \(\hspace{1ex}\frac{675}{999}\)
The answer is \(0.\overline{675}\)
\(\textbf{11)}\) \(\hspace{1ex}\frac{5}{33}\)
The answer is \(0.\overline{15}\)
Challenge Problems
\(\textbf{12)}\) \(\hspace{1ex}0.0\overline{5}\)
The answer is \(\frac{1}{18}\)
\(\textbf{13)}\) \(\hspace{1ex}0.\overline{98}-0.\overline{88}\)
The answer is \(0.\overline{10}=\displaystyle\frac{10}{99}\)
\(\textbf{14)}\) \(\hspace{1ex}0.\overline{10}-0.\overline{01}\)
The answer is \(0.\overline{09}=\displaystyle\frac{9}{99}=\frac{1}{11}\)
See Related Pages\(\)
