Terminal Decimal Representation Analysis
A fraction $ \frac{p}{q} $, where $ p $ and $ q $ are integers with no common factors other than 1, results in a terminal decimal representation if and only if the prime factorization of the denominator $ q $ consists only of the prime numbers 2 and 5.
Fraction Denominator Analysis
We examine the prime factors of the denominator for each given fraction:
- Option 1: $ \frac{2}{7} $
- Denominator: $ 7 $
- Prime Factors: $ 7 $
- Conclusion: Contains a prime factor other than 2 or 5. Not terminal.
- Option 2: $ \frac{2}{9} $
- Denominator: $ 9 $
- Prime Factors: $ 3 \times 3 = 3^2 $
- Conclusion: Contains a prime factor other than 2 or 5. Not terminal.
- Option 3: $ \frac{2}{3} $
- Denominator: $ 3 $
- Prime Factors: $ 3 $
- Conclusion: Contains a prime factor other than 2 or 5. Not terminal.
- Option 4: $ \frac{2}{5} $
- Denominator: $ 5 $
- Prime Factors: $ 5 $
- Conclusion: Denominator only contains the prime factor 5. Terminal.
Identifying the Terminal Decimal
Based on the analysis, the fraction $ \frac{2}{5} $ has a denominator whose only prime factor is 5. Therefore, it has a terminal decimal representation.
Similar Questions
- How many digits will be there to the right of the decimal point in the product of 99.75 and 0.05554?
- How will you write 2.6 years in years, months and days?
- Solve the following.
$3.142 + 3.61 - 2.12 + 4 - 7.6 =$ ? - 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.
$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03} \times \frac{1}{0.003}$- When 0.434343..... is converted into a fraction, then the result will be:
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 \(5\left( {1 - \frac{x}{5}} \right) - (5 - x) - \frac{1}{{200}}{\rm{of (20 - x) = 0}}{\rm{.08}}\) ?
