NCERT Solutions For Class 10 Math Chapter – 1 Exercies – 1.4

NCERT Solutions For Class 10 Math Chapter – 1 Exercise – 1.4

 

Q1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non – terminating repeating decimal.

  • 13/3125
  • 17/8
  • 64/455
  • 15/1600
  • 29/343
  • 23/22x 52
  • 129/22x 57 x 75
  • 6/15
  • 35/50
  • 77/210

Solution:-

 

  • 3125 = 5 x 5 x 5 x 5 x 5

Terminating.

  • 8 = 2 x 2 x 2

Terminating

  • 455 = 5 x 7 x 13

Non – terminating.

  • 1600 = 2 x 2 x 2 x 2 x 2 x 2 x  5 x 5

Terminating

  • 343 = 7 X  7 X 7

Non – terminating

 

  • Terminating
  • Non – terminating
  • Terminating
  • 10 = 2 x 5

Terminating

  • 30 = 2 x 3 x
    5

Non  – terminating

 

Q2. Write down the decimal expression of those rational numbers in Question 1 above which have terminating decimal expansions.

Solution:-

 

  • 13/3125 = 0.00416
  • 17/8 = 2.125
  • 23/2252= 0.115
  • 6/15 = 0.4
  • 35/50 = 0.7

 

Q3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational and of the form p , q you say , about the prime factors of q?

  • 123456789
  • 12012001200012000…
  • 12345678

Solution:-

 

  • Since this number has a terminating decimal expansion It is a rational number of the form p/q and q is the form 2mx 5n .
  • The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number.
  • Since the decimal expansion is non – terminating recurring the given number is a rational number of the form p/q and q is not of the the form 2mx  5n.

 

 

NCERT Solutions For Class 10 Math Chapter – 1 Exercise – 1.4   Q1. Without actually performing the long division, state…