Convert Repeating Decimal to Fraction
The problem requires converting the repeating decimal $0.5\overline{32}$ into an equivalent fraction. The digits '32' repeat indefinitely.
Decimal to Fraction Conversion Steps
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Let the repeating decimal be represented by $x$.
$x = 0.5323232...$
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Multiply $x$ by 10 to shift the decimal point just before the repeating block.
$10x = 5.323232...$ (Equation 1)
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Multiply $x$ by $1000$ (10 times $10^2$, where 2 is the number of repeating digits) to shift the decimal point to the end of the first repeating block.
$1000x = 532.323232...$ (Equation 2)
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Subtract Equation 1 from Equation 2 to eliminate the repeating decimal part.
$ \begin{array}{rcrcr} 1000x & = & 532 & . & 323232... \\ - 10x & = & 5 & . & 323232... \\ \hline 990x & = & 527 & . & 000000... \end{array} $
This simplifies to $990x = 527$.
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Solve for $x$ by dividing both sides by 990.
$x = \frac{527}{990}$
The fraction equivalent to $0.5\overline{32}$ is $\frac{527}{990}$. This corresponds to Option 4.
Similar Questions
- Solve the following.
$3.142 + 3.61 - 2.12 + 4 - 7.6 =$ ? What will the value of the following be (correct to three decimal points)?
$160.342 - 32.124$
Arrange the following numbers in their increasing order.
(1) $-0.96$
(2) $0.83$
(3) $0.24$
(4) $-0.64$
(5) $0.58$
- Which of the following has terminal decimal representation?
- The value of $0.\overline{23} + 0.\overline{22}$ is:
- If the value of $\frac{1}{36.18}$ is $0.0276$, then what is the value of $\frac{1}{0.0003618}$?
Simplify the given expression.
$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03} \times \frac{1}{0.003}$- When 0.434343..... is converted into a fraction, then the result will be:
- How will you write 2.84 hours in hours, minutes and seconds?
- Select the option that expresses $5.\overline{6}$ as a fraction.
Important Questions from Decimals
What is the result when 0.129129129… is converted to a fraction?
Which of the following statement(s) is/are correct?
I. (3/11) > 0.3
II. (7/8) > 0.86
The value of \(1.\overline{3}+0.\overline{69}-0.5\overline{23}\) is equal to:
The value of \(0.\bar 4 + 0.5 \bar 9 - 0.4 \overline{23}\) is equal to:
If 19 × 23 = 437, then find the value of (190 × 0.023).
