Podcast
Questions and Answers
What is the prime factorization of the number represented by the product 38 × 2 × 25 × 39 × 50?
What is the prime factorization of the number represented by the product 38 × 2 × 25 × 39 × 50?
How many zeros are present in the product of 38 × 2 × 25 × 39 × 50?
How many zeros are present in the product of 38 × 2 × 25 × 39 × 50?
What is the L.C.M. of the numbers 1296 and 2520?
What is the L.C.M. of the numbers 1296 and 2520?
Which of the following represents the H.C.F. of the numbers 1296 and 2520?
Which of the following represents the H.C.F. of the numbers 1296 and 2520?
Signup and view all the answers
Which is the minimum distance that three people walking 40 cm, 42 cm, and 45 cm per step must cover to be in sync?
Which is the minimum distance that three people walking 40 cm, 42 cm, and 45 cm per step must cover to be in sync?
Signup and view all the answers
What is the largest number that can divide 1251, 9377, and 15628 while leaving remainders of 1, 2, and 3 respectively?
What is the largest number that can divide 1251, 9377, and 15628 while leaving remainders of 1, 2, and 3 respectively?
Signup and view all the answers
When 16, 20, and 24 are divided by a certain smallest number, they leave a remainder of 5. What is that number?
When 16, 20, and 24 are divided by a certain smallest number, they leave a remainder of 5. What is that number?
Signup and view all the answers
What is the expression representing the composite nature of the product 7 × 11 × 15 + 15?
What is the expression representing the composite nature of the product 7 × 11 × 15 + 15?
Signup and view all the answers
How do you define ascending order when comparing irrational numbers?
How do you define ascending order when comparing irrational numbers?
Signup and view all the answers
What is the first step in comparing irrational numbers with different indexes?
What is the first step in comparing irrational numbers with different indexes?
Signup and view all the answers
Which of the following best describes descending order for irrational numbers?
Which of the following best describes descending order for irrational numbers?
Signup and view all the answers
What is required to convert irrational numbers to the same index?
What is required to convert irrational numbers to the same index?
Signup and view all the answers
If you need to compare $3 ext{ }24$, $3 ext{ }56$, and $3 ext{ }29$, what is assumed about their radical values?
If you need to compare $3 ext{ }24$, $3 ext{ }56$, and $3 ext{ }29$, what is assumed about their radical values?
Signup and view all the answers
What is the HCF of 26 and 91?
What is the HCF of 26 and 91?
Signup and view all the answers
What is the product of the two numbers 336 and 54?
What is the product of the two numbers 336 and 54?
Signup and view all the answers
Which expression correctly represents the LCM of 26 and 91?
Which expression correctly represents the LCM of 26 and 91?
Signup and view all the answers
What is the calculated HCF of 336 and 54?
What is the calculated HCF of 336 and 54?
Signup and view all the answers
Verify the relationship between LCM and HCF for the numbers 510 and 92.
Verify the relationship between LCM and HCF for the numbers 510 and 92.
Signup and view all the answers
Which collection of numbers is prime?
Which collection of numbers is prime?
Signup and view all the answers
What is the value of the LCM when calculating between 336 and 54?
What is the value of the LCM when calculating between 336 and 54?
Signup and view all the answers
What relationship holds true for HCF and LCM of two numbers?
What relationship holds true for HCF and LCM of two numbers?
Signup and view all the answers
What type of decimal expansion does the rational number $\frac{343}{73}$ have?
What type of decimal expansion does the rational number $\frac{343}{73}$ have?
Signup and view all the answers
What can be determined about the rational number $\frac{3125}{8}$?
What can be determined about the rational number $\frac{3125}{8}$?
Signup and view all the answers
Which rational number will have a terminating decimal expansion?
Which rational number will have a terminating decimal expansion?
Signup and view all the answers
What type of decimal expansion does the rational number $\frac{129}{2 \times 5^7 \times 75}$ have?
What type of decimal expansion does the rational number $\frac{129}{2 \times 5^7 \times 75}$ have?
Signup and view all the answers
The rational number $\frac{17}{23}$ results in which type of decimal expansion?
The rational number $\frac{17}{23}$ results in which type of decimal expansion?
Signup and view all the answers
For the rational number $\frac{50}{210}$, what can be inferred about its decimal expansion?
For the rational number $\frac{50}{210}$, what can be inferred about its decimal expansion?
Signup and view all the answers
What is the decimal expansion type of the rational number $\frac{2^2 \times 5^2}{15}$?
What is the decimal expansion type of the rational number $\frac{2^2 \times 5^2}{15}$?
Signup and view all the answers
Which of the following options indicates a rational number with a non-terminating repeating decimal expansion?
Which of the following options indicates a rational number with a non-terminating repeating decimal expansion?
Signup and view all the answers
What is the HCF of 420, 130, and 600?
What is the HCF of 420, 130, and 600?
Signup and view all the answers
Which of the following forms can a rational number have if its decimal expansion terminates?
Which of the following forms can a rational number have if its decimal expansion terminates?
Signup and view all the answers
If the prime factorization of the denominator $b$ is not of the form $2^m5^n$, what type of decimal expansion does the rational number $ rac{a}{b}$ have?
If the prime factorization of the denominator $b$ is not of the form $2^m5^n$, what type of decimal expansion does the rational number $ rac{a}{b}$ have?
Signup and view all the answers
Which calculation is correct for finding HCF using a divisor?
Which calculation is correct for finding HCF using a divisor?
Signup and view all the answers
Which decimal number corresponds to the rational number $ rac{875}{10000}$?
Which decimal number corresponds to the rational number $ rac{875}{10000}$?
Signup and view all the answers
What can be deduced if a rational number has a prime factorization of the denominator $b$ as $2^m5^n$?
What can be deduced if a rational number has a prime factorization of the denominator $b$ as $2^m5^n$?
Signup and view all the answers
Which statement correctly describes the transition from $ rac{a}{b}$ to its equivalent rational number using terminating decimals?
Which statement correctly describes the transition from $ rac{a}{b}$ to its equivalent rational number using terminating decimals?
Signup and view all the answers
Which example shows a rational number with a terminating decimal expansion?
Which example shows a rational number with a terminating decimal expansion?
Signup and view all the answers
Study Notes
Prime Factorization and Zeros
- Number of zeros in the product of 38 × 2 × 25 × 39 × 50 is determined by the prime factors of 2 and 5.
- Prime factorization gives power of 2 as 3 and power of 5 as 4.
- Minimum(3, 4) = 3, resulting in three zeros.
LCM and HCF Calculation
- LCM of 1296 and 2520 can be derived from their prime factorizations.
- 1296 = (2^4 × 3^4) and 2520 = (2^3 × 3^2 × 5 × 7).
- LCM = (2^4 × 3^4 × 5 × 7 = 45360).
- HCF = (2^3 × 3^2 = 72).
HCF Application
- To find the largest number that divides 1251, 9377, and 15628 with respective remainders of 1, 2, and 3, adjust these values down to 1250, 9375, and 15625.
- HCF of these adjusted numbers is 625.
Composite Numbers
- 7 × 11 × 15 + 15 can be expressed in factored form to show it is composite: ((7 × 11 + 1) × 15).
- This approach validates the number as composite through identifiable factors.
HCF and LCM Product Verification
- To verify ( \text{HCF} × \text{LCM} = \text{Product of two numbers} ), calculations with pairs (e.g., 510 and 92) show this holds true.
- HCF(510, 92) = 10 and LCM(510, 92) = 23460 leads to confirmation of the identity.
Decimal Expansion Theorem
- For a rational number x = a/b, if the prime factorization of b is of the form (2^m5^n), then x has a terminating decimal expansion.
- Examples illustrate this with conversions demonstrating the factorization forms.
Irrational Numbers Comparison
- To organize irrational numbers in ascending or descending order, convert to a common index through the least common multiple.
- This method allows the comparison of differing- index radicals.
Termination of Decimal Expansions
- Rational numbers structured as ( \frac{p}{q} ) where q fits (2^m5^n) will have terminating decimal expansions.
- Numbers failing this test will yield non-terminating repeating decimals.
Rational Number Classification
- Distinguishing between terminating and non-terminating decimal expansions can be done through the structure of the denominator in fractions.
- This classification is fundamental for understanding and predicting decimal behavior in rational numbers.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers key concepts in prime factorization, the calculation of least common multiples (LCM), and highest common factors (HCF). It includes practical applications of these concepts to solve problems. Enhance your understanding of composite numbers and their properties through engaging questions.
