Converting Repeating Decimal to Fraction
To convert the repeating decimal $0.434343...$ into a fraction, follow these steps:
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Let the decimal be represented by a variable, for example, $x$. $x = 0.434343...$
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Identify the repeating block. The digits '43' repeat. Since there are 2 repeating digits, multiply the equation by $10^2 = 100$. $100x = 100 \times 0.434343...$ $100x = 43.434343...$
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Subtract the original equation ($x = 0.434343...$) from the new equation ($100x = 43.434343...$) to eliminate the decimal part. $100x - x = (43.434343...) - (0.434343...)$ $99x = 43$
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Solve for $x$ by dividing both sides by 99. $x = \frac{43}{99}$
Therefore, the fraction equivalent of the repeating decimal $0.434343...$ is $\frac{43}{99}$.
Final Result Verification
Comparing the result $\frac{43}{99}$ with the given options, Option 3 matches the calculated fraction.
Similar Questions
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- How will you write 2.6 years in years, months and days?
- Solve the following.
$3.142 + 3.61 - 2.12 + 4 - 7.6 =$ ? - Which of the following has terminal decimal representation?
- The value of $0.\overline{23} + 0.\overline{22}$ is:
- Simplify the given expression.
$0.25 \div 0.0025 \times 0.025 \times 2.5$ Simplify the given expression.
$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03} \times \frac{1}{0.003}$Arrange the following numbers in their increasing order.
(1) $-0.96$
(2) $0.83$
(3) $0.24$
(4) $-0.64$
(5) $0.58$
- $0.5\overline{32}$ is equivalent to the fraction:
- Select the option that expresses $5.\overline{6}$ as a fraction.
Important Questions from Decimals
The value of \(\frac{1}{4} + \frac{{[{{(20.35)}^2} - {{(8.35)}^2}] \times 0.0175}}{{{{(1.05)}^2} + (1.05)(27.65)}}\) is:
The value of \(0.4\overline 6 + 0.7\overline {23} - 0.3\overline 9 \times 0.\overline 7 \) is:
The value of \(\frac{48.3\times[(4.95)^2+4.95\times13.25]}{[(12.55)^2-(5.65)^2]\times19.8} \) is:
Find the value of (1.6) 3 - (0.9) 3 - (0.7) 3.
What is the value of x, if \(5\left( {1 - \frac{x}{5}} \right) - (5 - x) - \frac{1}{{200}}{\rm{of (20 - x) = 0}}{\rm{.08}}\) ?
