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
- 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) $0.58$
- 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:
- $0.5\overline{32}$ 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:
If 19 × 23 = 437, then find the value of (190 × 0.023).
