### 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…