Real Numbers – Class 10/ Extra Questions.

Chapter 1 of CBSE/NCERT Class 10 Mathematics is about Real numbers. Here in this lesson you can find out practice problems for this chapter.

CBSE CLASS 10 MATHEMATICS
Real Numbers/ Extra Questions – Chapter 1

Answer the following:

1. Write the following rational numbers in decimal form:
   i) 37/100
   ii) 24/50
2. Which of the following rational numbers have the terminating decimal expansion?
   i) 13/20
   ii) 37/40
3. Express each of the following as a product of its prime factors.
   i) 343
   ii) 1092
4. Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = Product of the two numbers.
   i) 27, 33
5. Find the LCM and HCF of the following integers by applying the Prime factorisation method?
   i) 14, 42, 70
   ii) 21, 27, 33

ANSWERS:

1. i) 37/100 = 0.37
   ii) 24/50 = 48/100 = 0.48
2. If the denominator has only factors of 2 and 5 , then it has terminating expansion.
   i) Here we have 20 = 2 x 2 x 5
   The prime factors of 20 are 2 and 5 only. Hence 13/20 has a terminating decimal expansion.
   ii) We have 40 = 2 x 2 x 2 x 5
   The prime factors of 40 are 2 and 5 only. Hence 37/40 has a terminating decimal expansion.
3. i) 343 = 7 x 7 x 7
   ii) 1092 = 2 x 2 x 3 x 7 x 13
4. i) We have 27 = 3 x 3 x 3
   33 = 3 x 11
   Therefore, LCM (27, 33) = 3 x 3 x 3 x 11 = 297
   HCF (27, 33) = 3
   Now LCM x HCF = 297 x 3 = 891
   Product of 27 and 33 = 27 x 33 = 891
   So verified.
5. i) First we can write as product of prime factors.
   14 = 2 x 7
   42 = 2 x 3 x 7
   70 = 2 x 5 x 7
   Therefore, HCF (14, 42, 70) = 2 x 7 = 14
   LCM (14, 42, 70) = 2 x 3 x 5 x 7 = 210
   ii) First we can write as product of prime factors.
   21 = 3 x 7
   27 = 3 x 3 x 3
   33 = 3 x 11
   Therefore, HCF (21, 27, 33) = 3
   LCM (21, 27, 33) = 3 x 3 x 3 x 7 x 11 = 2079.