2753
1. The decimal expansion of $\frac{17}{8}$ will be:
2761
2. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :
2748
3. The relation between their LCM and HCF, if numbers are positive integer.
2744
4. Express 0.125 in the form $\frac{p}{q}$.
2742
5. Express 0.104 in the form $\frac{p}{q}$.
2747
6. If $\boldsymbol{a}$ and $\boldsymbol{b}$ are two positive integers, then the relation between their LCM and HCF will be:
2741
7. Express 0.375 in the form $\frac{p}{q}$.
2755
8. . The LCM of 8,9 and 25 will be:
2743
9. Explain 0.0875 in the form $\frac{p}{q}$.
2745
10. Express 15.75 in the form $\frac{p}{q}$.
2746
11. The relation between HCF and LCM of 12 and 20 will be:
2757
12. The LCM of 26 and 91 will be:
2762
13. The decimal expansion of the rational number $\frac{7}{5}$ will terminate after:
2760
14. For some integer $m$, every even integer is of the form
2756
15. The HCF of 36 and 78 will be:
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: