can be written in the form of:
Convert Repeating Decimal to Fraction
The question asks to convert the repeating decimal $1.236576576...$ into a fraction. The repeating block is '576'.
Step-by-Step Conversion
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Let the number be x. So, $x = 1.236576576...$
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Identify the non-repeating part ('23') and the repeating part ('576'). There are 2 digits before the repeating block and 3 digits in the repeating block.
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Multiply x by $10^2 = 100$ to move the decimal point just before the repeating block:
$100x = 123.6576576...$ (Equation 1)
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Multiply x by $10^{(2+3)} = 10^5 = 100000$ to move the decimal point to the end of the first repeating block:
$100000x = 123657.6576576...$ (Equation 2)
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Subtract Equation 1 from Equation 2 to eliminate the repeating decimal part:
$100000x - 100x = 123657.6576576... - 123.6576576...$
$99900x = 123657 - 123$
$99900x = 123534$
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Solve for x:
$x = \frac{123534}{99900}$
This result matches option 3.
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?
- 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 $2$?
- Solve the following:
$(0.\overline{5} + 0.\overline{6} + 0.\overline{7} + 0.\overline{8}) = ?$ - 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.
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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:
