Check sibling questions

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Transcript

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 = πŸπŸ‘/(𝟐𝟎 Γ— πŸ“πŸ“) Multiplying and dividing by 25 = 13/(20 Γ— 55) Γ— πŸπŸ“/πŸπŸ“ = (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— πŸ“πŸ‘/πŸ“πŸ‘ = (17 Γ— 5^3)/(50 Γ— 23 Γ— 5^3 ) = (17 Γ— 125)/(𝟏 Γ— 23 Γ— 5^3 ) = (17 Γ— 125)/(1 Γ— (πŸ“ Γ— 𝟐)πŸ‘) = 2125/(𝟏𝟎)πŸ‘ = 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/(πŸπŸ” Γ— πŸ“πŸ) We multiply and divide the equation by 55 = 3/(26 Γ—51) Γ— πŸ“πŸ“/πŸ“πŸ“ = (3 Γ— 5^5)/(26 Γ— 51 Γ— 5^5 ) = (3 Γ— πŸ‘πŸπŸπŸ“)/(26 Γ— πŸ“^(𝟏+πŸ“) ) = (3 Γ— 3125)/(26 γ€–Γ— 5γ€—^6 ) = (3 Γ— 3125)/(𝟐 Γ— πŸ“)πŸ” = πŸ—πŸ‘πŸ•πŸ“/(𝟏𝟎)πŸ” = 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 Γ—52) Γ— πŸ“πŸ/πŸ“πŸ = (23 Γ— 5^1)/(23 Γ— 52 γ€–Γ— 5γ€—^1 ) = (23 Γ— 5)/(23 γ€–Γ— πŸ“γ€—^(𝟐 + 𝟏) ) = (23 Γ— 5)/(23 γ€–Γ— 5γ€—^3 ) = (23 Γ— 5)/((𝟐 Γ— γ€–πŸ“)γ€—^πŸ‘ ) = 115/(𝟏𝟎)πŸ‘ = 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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.