$(0.\overline{5} + 0.\overline{6} + 0.\overline{7} + 0.\overline{8}) = ?$
Solving Sum of Repeating Decimals
The question asks to find the sum of four repeating decimals: $0.\overline{5}$, $0.\overline{6}$, $0.\overline{7}$, and $0.\overline{8}$.
Repeating Decimal to Fraction Conversion
First, convert each repeating decimal into its fractional form. A repeating decimal of the form $0.\overline{d}$ is equivalent to the fraction $\frac{d}{9}$.
- $0.\overline{5} = \frac{5}{9}$
- $0.\overline{6} = \frac{6}{9}$
- $0.\overline{7} = \frac{7}{9}$
- $0.\overline{8} = \frac{8}{9}$
Summing the Fractions
Next, add these fractions together. Since they have a common denominator (9), we simply add the numerators:
$ \frac{5}{9} + \frac{6}{9} + \frac{7}{9} + \frac{8}{9} = \frac{5 + 6 + 7 + 8}{9} $
Simplifying the Result
Calculate the sum of the numerators:
$ 5 + 6 + 7 + 8 = 26 $
The sum is $\frac{26}{9}$.
Converting to Mixed Number
Finally, convert the improper fraction $\frac{26}{9}$ into a mixed number. Divide 26 by 9:
$ 26 \div 9 = 2 \text{ with a remainder of } 8 $
Therefore, the mixed number is $2\frac{8}{9}$.
Similar Questions
- The numerator of a fraction is increased by $20\%$ and the denominator is decreased by $50\%$. If the resultant fraction is $\frac{5}{6}$, then what will be the original fraction?
- $1.236576576...$
can be written in the form of: - What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
- What is the positive difference between $\frac{5}{16}$ and its reciprocal?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
Important Questions from Fractions
Which fraction among the following is the least ?
\(\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}\)
Find the value of the following expression:
\(\frac{{3 \div 1 \times 2 + 5 - 2}}{{3 \times 3 - 2}}\)
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
