2762
1. The decimal expansion of the rational number $\frac{7}{5}$ will terminate after:
2758
2. The LCM of 45 and 75 will be:
2753
3. The decimal expansion of $\frac{17}{8}$ will be:
2750
4. If HCF of 124 and 148 is 4 , then its LCM is:
2757
5. The LCM of 26 and 91 will be:
2743
6. Explain 0.0875 in the form $\frac{p}{q}$.
2747
7. If $\boldsymbol{a}$ and $\boldsymbol{b}$ are two positive integers, then the relation between their LCM and HCF will be:
2744
8. Express 0.125 in the form $\frac{p}{q}$.
2761
9. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :
2746
10. The relation between HCF and LCM of 12 and 20 will be:
2756
11. The HCF of 36 and 78 will be:
2748
12. The relation between their LCM and HCF, if numbers are positive integer.
2759
13. Which of the following is rational number?
2754
14. The LCM of 12,15 and 21 will be:
2741
15. Express 0.375 in the form $\frac{p}{q}$.
Chapter 1 of Class 10 Maths, Real Numbers, forms the basis of advanced mathematics. Here are the key topics covered in this chapter:
The Fundamental Theorem of Arithmetic states that every composite number can be expressed (factorized) as a product of prime numbers in a unique way, except for the order of primes. For example:
Euclid's Division Lemma states that for any two positive integers a and b, there exist unique integers q and r such that:
a = bq + r, where 0 ≤ r < b
Applications include finding the HCF of two numbers.
Proving that certain numbers, such as \( \sqrt{2} \), \( \sqrt{3} \), and \( \sqrt{5} \), are irrational involves using proof by contradiction and the properties of prime factorization.
Rational numbers have either a terminating or repeating decimal expansion. For example:
Understanding Real Numbers is crucial as it lays the foundation for higher-level mathematical concepts and problem-solving skills. The topics in this chapter are also frequently tested in board exams.
Looking for more practice? Check out these resources: