2760
1. For some integer $m$, every even integer is of the form
2753
2. The decimal expansion of $\frac{17}{8}$ will be:
2745
3. Express 15.75 in the form $\frac{p}{q}$.
2758
4. The LCM of 45 and 75 will be:
2754
5. The LCM of 12,15 and 21 will be:
2762
6. The decimal expansion of the rational number $\frac{7}{5}$ will terminate after:
2751
7. Which of the following number will be terminating?
2748
8. The relation between their LCM and HCF, if numbers are positive integer.
2744
9. Express 0.125 in the form $\frac{p}{q}$.
2759
10. Which of the following is rational number?
2763
11. 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:
2750
12. If HCF of 124 and 148 is 4 , then its LCM is:
2743
13. Explain 0.0875 in the form $\frac{p}{q}$.
2761
14. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :
2764
15. The HCF of 870 and 225 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: