NCERT full solutions here you can find full detailed solutions for all the questions with proper format. class 10 maths ncert solutions chapter 1 exercise 1.4
You can see the solution for complete chapter here –
-
Complete 10th Class Maths Solution
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.1 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.2 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.3 Real Number
CHAPTER 1 REAL NUMBERS – EXERCISE:-1.4
QUE:- WITHOUT ACTUAALY PERFORMING THE LONG DIVISION, STATE WHETHER THE FOLLOWING RATIONAL
NUMBERS WILL HAVE A TERMINATING DECIMAL EXAPSION OR A NON TERMINATING REPEATING DECIMAL EXANSION:
(i)13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 (vi) 23/2³5² (vii) 129/2²5power(7)7power(5) (viii) 6/15 (ix)35/50 (x)77/210
SOL:-
(i) 13/3125
3125=5power(5)
the denomenator is the form 5 power(m).
hence ,the decimal expansion of 13/3125 is terminating.
(ii) 17/8
8=2³
the denominator is of the form 2 power(m)
hence ,the decimal expansion of 17/8 is terminating.
(iii) 64/455
455=5×7×13
since the denominator is not in the form 2 power(m)×5 power(n), and it also contain 7 and 13 as its factors,
its decimal expansion will be non -termeneting repeating.
(iv) 15/1600
1600=2power(6)×5²
the denominator is in the form 2 power(m)×5 power(n).
hence ,the decimal expansion of 15/1600 is terminating.
(v) 29/343
343=7³
since the denominator is not in the form 2 power(m)×5 power(n), and it also contain 7 as its factors,
its decimal expansion will be non -termeneting repeating.
(vi) 23/2³5²
the denominator is in the form 2 power(m)×5 power(n),
hence ,the decimal expansion of 23/2³5² is terminating.
(vii) 129/2²5power(7)7power(5)
since the denominator is not in the form 2 power(m)×5 power(n), and it also contain 7 as its factors,
its decimal expansion will be non -termeneting repeating.
(viii) 6/15
6/15=(2×3)/(3×5)=2/5
the denomenator is the form 5 power(m).
hence ,the decimal expansion of 6/15 is terminating.
(ix) 35/50
35/50=7×5/10×5
10=2×5
the denominator is in the form 2 power(m)×5 power(n).
hence ,the decimal expansion of 35/50 is terminating.
(x) 77/210
77/210=11×7/30×7=11/30
30=2×3×5
since the denominator is not in the form 2 power(m)×5 power(n), and it also contain 3 as its factors,
its decimal expansion will be non -termeneting repeating.
QUE:-WRITE DOWN THE DECIMAL EXPANSIONS OF THOSE RATIONAL NUMBERS IN QUESTION 1 ABOVE WHICH HAVE TERMENATING DECIMAL EXPANSITION
SOL:-
(i) 13/3125 =0.00416 31225)13.00000(0.00416
0
130
0
1300
0
13000
12500
5000
3125
18750
18750
×
(ii) 17/8 = 2.125 8) 17 (2.125
– 16
10
– 08
20
– 16
40
40
×
(iv) 15/1600=0.009375 1600)15.000000(0.00416
– 0
150
– 0
1500
0
15000
– 14400
6000
– 4800
12000
– 11200
8000
– 8000
×
(vi) 23/2³5²=23/200=0.115 200) 23 (0.115
– 0
230
– 200
300
– 200
1000
1000
×
(viii) 16/15=2×3/3×5=2/5=0.4 5) 2 .0 (0.4
0
20
– 20
×
(ix) 35/50=0.7 50 )35.0(0.7
0
350
350
×
QUE:- THE FOLLOWING REAL NUMBERS HAVE DECIMAL EXPENSION AS GIVEN BELOW. IN EACH CASE , DECIDE WHETHER TEY ARE RATIONAL OR NOT IF THEY ARE RATIONAL , AND OF THE FORM P/Q ,WHAT CAN SAY ABOUT THE PRIME FACTORE OF Q ?
(i) 43.123456789 (ii)0.120120012000120000…….. (iii) 43.123456789
SOL:-
(i) 43.123456789
since this number has a terminating decimal expension, it is a rational number of the form p/q and q of the form 2 power(m)×5 power(n),
the prime factore of q will be either 2 or 5 or both.
(ii) 0.120120012000120000……….
the decimal expresion is neither terminating nor recuring. therefore, the given number is an irrational number .
(iii) 43.123456789
since the decimal expension is non-terminating recurring the given number is a rational number of tha form p/q
q is not of the form 2 power(m)×5 power(n),
the prime factors of q will also have a factor other than 2 or 5.
You can see the solution for complete chapter here –
Tags – class 10th maths solution, maths solution for class 10th, 10th class maths solution, solution for class 10th, maths 10th class solution, maths chapter 1 solution, 1.4 solution 10th class.
