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
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- 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?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- 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.
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Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
