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.