Page 1 Exercise - 1C 1. Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form. (i) (ii) (iii) (iv) (v) (vi) Answer: (i) = = = 0.115 We know either 2 or 5 is not a factor of 23, so it is in its simplest form Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (ii) = = = = 0.192 We know 5 is not a factor of 23, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iii) = = = = 0.21375 We know either 2 or 5 is not a factor of 171, so it is in its simplest form. Page 2 Exercise - 1C 1. Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form. (i) (ii) (iii) (iv) (v) (vi) Answer: (i) = = = 0.115 We know either 2 or 5 is not a factor of 23, so it is in its simplest form Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (ii) = = = = 0.192 We know 5 is not a factor of 23, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iii) = = = = 0.21375 We know either 2 or 5 is not a factor of 171, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iv) = = = = 0.009375 We know either 2 or 5 is not a factor of 15, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (v) = = = = 0.053125 We know either 2 or 5 is not a factor of 17, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (vi) = = = = 0.00608 We know either 2 or 5 is not a factor of 19, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. 2. Without actual division show that each of the following rational numbers is a non- terminating repeating decimal. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) Answer: (i) We know either 2 or 3 is not a factor of 11, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non terminating repeating decimal. (ii) We know 2, 3 or 5 is not a factor of 73, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (iii) We know 2, 5 or 7 is not a factor of 129, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (iv) = We know either 5 or 7 is not a factor of 9, so it is in its simplest form. Moreover, (5 × 7) m × 5 n ) Hence, the given rational is non-terminating repeating decimal. Page 3 Exercise - 1C 1. Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form. (i) (ii) (iii) (iv) (v) (vi) Answer: (i) = = = 0.115 We know either 2 or 5 is not a factor of 23, so it is in its simplest form Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (ii) = = = = 0.192 We know 5 is not a factor of 23, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iii) = = = = 0.21375 We know either 2 or 5 is not a factor of 171, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iv) = = = = 0.009375 We know either 2 or 5 is not a factor of 15, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (v) = = = = 0.053125 We know either 2 or 5 is not a factor of 17, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (vi) = = = = 0.00608 We know either 2 or 5 is not a factor of 19, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. 2. Without actual division show that each of the following rational numbers is a non- terminating repeating decimal. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) Answer: (i) We know either 2 or 3 is not a factor of 11, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non terminating repeating decimal. (ii) We know 2, 3 or 5 is not a factor of 73, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (iii) We know 2, 5 or 7 is not a factor of 129, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (iv) = We know either 5 or 7 is not a factor of 9, so it is in its simplest form. Moreover, (5 × 7) m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (v) = = = We know 2, 3 or 5 is not a factor of 11, so is in its simplest form. m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (vi) = We know either 3 or 7 is not a factor of 32, so it is in its simplest form. Moreover, (3 × 7 2 m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (vii) = We know 7 is not a factor of 29, so it is in its simplest form. Moreover, 7 3 m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (viii) = We know 5, 7 or 13 is not a factor of 64, so it is in its simplest form. m × 5 n ) Hence, the given rational is non-terminating repeating decimal. 3. Express each of the following as a rational number in its simplest form: (iii) (iv) (v) (vi) Answer: (i) Let x = x = 0.888 10x = 8.888 On subtracting equation (1) from (2), we get 9x = 8 x = 0.8 = (ii) Let x = x = 2.444 10x = 24.444 On subtracting equation (1) from (2), we get 9x = 22 x = 2.4 = (iii) Let x = x = 0.2424 100x = 24.2424 Page 4 Exercise - 1C 1. Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form. (i) (ii) (iii) (iv) (v) (vi) Answer: (i) = = = 0.115 We know either 2 or 5 is not a factor of 23, so it is in its simplest form Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (ii) = = = = 0.192 We know 5 is not a factor of 23, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iii) = = = = 0.21375 We know either 2 or 5 is not a factor of 171, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (iv) = = = = 0.009375 We know either 2 or 5 is not a factor of 15, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (v) = = = = 0.053125 We know either 2 or 5 is not a factor of 17, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. (vi) = = = = 0.00608 We know either 2 or 5 is not a factor of 19, so it is in its simplest form. Moreover, it is in the form of (2 m × 5 n ). Hence, the given rational is terminating. 2. Without actual division show that each of the following rational numbers is a non- terminating repeating decimal. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) Answer: (i) We know either 2 or 3 is not a factor of 11, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non terminating repeating decimal. (ii) We know 2, 3 or 5 is not a factor of 73, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (iii) We know 2, 5 or 7 is not a factor of 129, so it is in its simplest form. Moreover, m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (iv) = We know either 5 or 7 is not a factor of 9, so it is in its simplest form. Moreover, (5 × 7) m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (v) = = = We know 2, 3 or 5 is not a factor of 11, so is in its simplest form. m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (vi) = We know either 3 or 7 is not a factor of 32, so it is in its simplest form. Moreover, (3 × 7 2 m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (vii) = We know 7 is not a factor of 29, so it is in its simplest form. Moreover, 7 3 m × 5 n ) Hence, the given rational is non-terminating repeating decimal. (viii) = We know 5, 7 or 13 is not a factor of 64, so it is in its simplest form. m × 5 n ) Hence, the given rational is non-terminating repeating decimal. 3. Express each of the following as a rational number in its simplest form: (iii) (iv) (v) (vi) Answer: (i) Let x = x = 0.888 10x = 8.888 On subtracting equation (1) from (2), we get 9x = 8 x = 0.8 = (ii) Let x = x = 2.444 10x = 24.444 On subtracting equation (1) from (2), we get 9x = 22 x = 2.4 = (iii) Let x = x = 0.2424 100x = 24.2424 On subtracting equation (1) from (2), we get 99x = 24 x = 0.24 = (iv) Let x = x = 0.1212 100x = 12.1212 On subtracting equation (1) from (2), we get 99x = 12 x = 0.12 = (v) Let x = x = 2.2444 10x = 22.444 100x = 224.444 On subtracting equation (2) from (3), we get 90x = 202 x = = = (vi) Let x = x = 0.3656565 10x = 3.656565 1000x = 365.656565 On subtracting equation (2) from (3), we get 990x = 362 x = = =Read More

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