2744
1. Express 0.125 in the form $\frac{p}{q}$.
2754
2. The LCM of 12,15 and 21 will be:
2747
3. If $\boldsymbol{a}$ and $\boldsymbol{b}$ are two positive integers, then the relation between their LCM and HCF will be:
2763
4. If two positive integers $a$ and $b$ can be expressed as $a=x^{3} y^{2}$ and $b=x y^{3} ; x, y$ being prime numbers, then $\operatorname{HCF}(a, b)$ is:
2753
5. The decimal expansion of $\frac{17}{8}$ will be:
2759
6. Which of the following is rational number?
2748
7. The relation between their LCM and HCF, if numbers are positive integer.
2757
8. The LCM of 26 and 91 will be:
2752
9. . If $H C F$ of 35 and 84 is 7 , then find its LCM:
2746
10. The relation between HCF and LCM of 12 and 20 will be:
2751
11. Which of the following number will be terminating?
2764
12. The HCF of 870 and 225 will be:
2761
13. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :
2762
14. The decimal expansion of the rational number $\frac{7}{5}$ will terminate after:
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: