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Decimal Expansion

Question 1 (i)
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Question 1 (ii) Deleted for CBSE Board 2024 Exams

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Chapter 1 Class 10 Real Numbers

Serial order wise

Last updated at May 29, 2023 by Teachoo

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 Question 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 Question 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 Question 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