Convert the following decimal numbers in the form of . (i) 12.6 (ii) 0.0120 (iii) (iv) (v) (vi) (vii) (viii) (ix)

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KnowledgeBoat · Accepted Answer

(i) Given: 12.6 ⇒ Hence, . (ii) Given: 0.0120 ⇒ Hence, . (iii) Given: Let x = = 3.0525252… Multiplying both sides by 10 (1 non-repeating digit) : ⇒ 10x = 30.5252… Multiplying both sides by 1000 (1 non-repeating + 2 repeating digits) : ⇒ 1000x = 3052.5252… Subtracting : 1000x - 10x = 3052.5252... - 30.5252... 990x = 3022 ⇒ x = ⇒ x = Hence, . (iv) Given: Let x = = 1.2353535… Multiplying both sides by 10 (1 non-repeating digit) : ⇒ 10x = 12.353535… Multiplying both sides by 1000 (1 non-repeating + 2 repeating digits) : ⇒ 1000x = 1235.353535… Subtracting : ⇒ 1000x - 10x = 1235.353535… - 12.353535… ⇒ 990x = 1223 ⇒ x = . Hence, . (v) Given, Let x = = 0.232323… Multiplying both sides by 100 (2 repeating digits) : ⇒ 100x = 23.2323… Subtracting : ⇒ 100x - x = 23.2323… - 0.2323… ⇒ 99x = 23 ⇒ x = . Hence, . (vi) Given, Let x = = 2.05555… Multiplying both sides by 10 (1 non-repeating digit) : ⇒ 10x = 20.5555… Multiplying both sides by 100 (1 non-repeating + 1 repeating digit) : ⇒ 100x = 205.5555… Subtracting : ⇒ 100x - 10x = 205.5555… - 20.5555… ⇒ 90x = 185 ⇒ x = . Hence, . (vii) Given, Let x = = 2.12555… Multiplying both sides by 100 (2 non-repeating digits) : ⇒ 100x = 212.555… Multiplying both sides by 1000 (2 non-repeating + 1 repeating digit) : ⇒ 1000x = 2125.555… Subtracting : ⇒ 1000x - 100x = 2125.555… - 212.555… ⇒ 900x = 1913 ⇒ x = . Hence, . (viii) Given, Let x = = 3.12555… Multiplying both sides by 100 (2 non-repeating digits) : ⇒ 100x = 312.555… Multiplying both sides by 1000 (2 non-repeating + 1 repeating digit) : ⇒ 1000x = 3125.555… Subtracting : ⇒ 1000x - 100x = 3125.555… - 312.555… ⇒ 900x = 2813 ⇒ x = . Hence, . (ix) Given, Let x = = 2.1625 1625… Multiplying both sides by 10000 (4 repeating digits) : ⇒ 10000x = 21625.1625… Subtracting : ⇒ 10000x - x = 21625.1625… - 2.1625… ⇒ 9999x = 21623 ⇒ x = . Hence, .

Mathematics

Convert the following decimal numbers in the form of . (i) 12.6 (ii) 0.0120 (iii) (iv) (v) (vi) (vii) (viii) (ix)

Whole Numbers

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