# 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 MATHEMATICSReal Numbers/ Extra Questions – Chapter 1**

**Answer the following:**

- Write the following rational numbers in decimal form:

i) 37/100

ii) 24/50 - Which of the following rational numbers have the terminating decimal expansion?

i) 13/20

ii) 37/40 - Express each of the following as a product of its prime factors.

i) 343

ii) 1092 - 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 - Find the LCM and HCF of the following integers by applying the Prime factorisation method?

i) 14, 42, 70

ii) 21, 27, 33

**ANSWERS:**

- i) 37/100 = 0.37

ii) 24/50 = 48/100 = 0.48 - 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. - i) 343 = 7 x 7 x 7

ii) 1092 = 2 x 2 x 3 x 7 x 13 - 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. - 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.