Question 2 - Decimal Expansion - Chapter 1 Class 10 Real Numbers

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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 = 𝟏𝟑/(𝟐𝟎 × 𝟓𝟓) Multiplying and dividing by 25 = 13/(20 × 55) × 𝟐𝟓/𝟐𝟓 = (13 × 25)/(20 × 55 × 25) = (13 × 32)/(1 × 55 × 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 × 23) Multiplying and dividing by 53 = 17/(50 × 23) × 𝟓𝟑/𝟓𝟑 = (17 × 5^3)/(50 × 23 × 5^3 ) = (17 × 125)/(𝟏 × 23 × 5^3 ) = (17 × 125)/(1 × (𝟓 × 𝟐)𝟑) = 2125/(𝟏𝟎)𝟑 = 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/(𝟐𝟔 × 𝟓𝟏) We multiply and divide the equation by 55 = 3/(26 ×51) × 𝟓𝟓/𝟓𝟓 = (3 × 5^5)/(26 × 51 × 5^5 ) = (3 × 𝟑𝟏𝟐𝟓)/(26 × 𝟓^(𝟏+𝟓) ) = (3 × 3125)/(26 〖× 5〗^6 ) = (3 × 3125)/(𝟐 × 𝟓)𝟔 = 𝟗𝟑𝟕𝟓/(𝟏𝟎)𝟔 = 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 ×52) × 𝟓𝟏/𝟓𝟏 = (23 × 5^1)/(23 × 52 〖× 5〗^1 ) = (23 × 5)/(23 〖× 𝟓〗^(𝟐 + 𝟏) ) = (23 × 5)/(23 〖× 5〗^3 ) = (23 × 5)/((𝟐 × 〖𝟓)〗^𝟑 ) = 115/(𝟏𝟎)𝟑 = 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