Ex 1.4 , 2 (Method 1)
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
13/3125
From Ex 1.4, 1(i) , we know
13/3125 = ππ/(ππ Γ ππ)
Multiplying and dividing by 25
= 13/(20 Γ 55) Γ ππ/ππ
= (13 Γ 25)/(20 Γ 55 Γ 25)
= (13 Γ 32)/(1 Γ 55 Γ 25)
= 416/((10)5)
= 416/((100000))
= 0.00416
Ex 1.4, 2 (Method 2)
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
13/3125
13/3125 = 0.00416
Ex 1.4, 2 (Method 1)
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(ii) 17/8
From Ex1.4,1(ii), we know
17/8 = 17/(50 Γ 23)
Multiplying and dividing by 53
= 17/(50 Γ 23) Γ ππ/ππ
= (17 Γ 5^3)/(50 Γ 23 Γ 5^3 )
= (17 Γ 125)/(π Γ 23 Γ 5^3 )
= (17 Γ 125)/(1 Γ (π Γ π)π)
= 2125/(ππ)π
= 2125/((1000) )
= 2.125
Ex 1.4 , 2 (Method 2)
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(ii) 17/8
17/8 = 2.125
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(iii) 64/455
64/455 has non terminating decimal expansion
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(iv) 15/1600
From Ex1.4,1(iv), we know
15/1600 = 3/320
= 3/(ππ Γ ππ)
We multiply and divide the equation by 55
= 3/(26 Γ51) Γ ππ/ππ
= (3 Γ 5^5)/(26 Γ 51 Γ 5^5 )
= (3 Γ ππππ)/(26 Γ π^(π+π) )
= (3 Γ 3125)/(26 γΓ 5γ^6 )
= (3 Γ 3125)/(π Γ π)π
= ππππ/(ππ)π
= 9375/((1000000) )
= 0.009375
Ex 1.4 , 2 (Method 2)
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(iv) 15/1600
15/1600 = 3/320
= 0.009375
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(v) 29/343
29/343 has a non terminating decimal expansion
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(vi) 23/(23 5^2 )
23/(23 5^2 )
We multiply and divide the equation by 51
23/(23 5^2 )= 23/(23 Γ52) Γ ππ/ππ
= (23 Γ 5^1)/(23 Γ 52 γΓ 5γ^1 )
= (23 Γ 5)/(23 γΓ πγ^(π + π) )
= (23 Γ 5)/(23 γΓ 5γ^3 )
= (23 Γ 5)/((π Γ γπ)γ^π )
= 115/(ππ)π
= 115/((1000) )
= 0.115
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(vii) 129/(22 57 75)
129/(22 57 75) has a non terminating decimal expansion.
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(viii) 6/15
6/15 = 2/( 5)
= 0.4
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(ix) 35/50
35/50 = 7/10
= 0.7
Ex 1.4 , 2
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(x) 77/210
77/210 has a non terminating decimal expansion

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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