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
- 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.
$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03} \times \frac{1}{0.003}$- $0.5\overline{32}$ is equivalent to the fraction:
- 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:
Find the sum of \(\frac{0.01}{0.1}+\frac{0.1}{0.01}\)
