Without actual division, find whether the following rational numbers are terminating decimals or recurring decimals : (i) 13/45 (ii) −5/56 (iii) 7/125 (iv) −23/80 (v) −15/66. In case of terminating decimals, write their decimal expansions.

Question

KnowledgeBoat · Accepted Answer

The given number is in its lowest form. Prime factorization of denominator 45: 45 = 3 x 3 x 5 x 1 = 3² x 5 x 1 Denominator is not of the form 2^m x 5ⁿ, where m, n are non-negative integers. ∴ The given number is recurring decimal. The given number is in its lowest form. Prime factorization of denominator 56: 56 = 2 x 2 x 2 x 7 x 1 = 2³ x 7 x 1 Denominator is not of the form 2^m x 5ⁿ, where m, n are non-negative integers. ∴ The given number is recurring decimal. The given number is in its lowest form. Prime factorization of denominator 125: 125= 5 x 5 x 5 x 1 = 5³ x 1 = 5³ x 2⁰ Denominator is of the form 2^m x 5ⁿ, where m, n are non-negative integers. ∴ The given number is a terminating decimal and its decimal expansion is 0.056. The given number is in its lowest form. Prime factorization of denominator 80: 80 = 2 x 2 x 2 x 2 x 5 x 1 = 2⁴ x 5¹ Denominator is of the form 2^m x 5ⁿ, where m, n are non-negative integers. ∴ The given number is a terminating decimal and its decimal expansion is -0.2875. The given number is in its lowest form. Prime factorization of denominator 66: 66 = 2 x 3 x 11 x 1 = 2 x 3 x 11 Denominator is not of the form 2^m x 5ⁿ, where m, n are non-negative integers. ∴ The given number is recurring decimal.

Mathematics

Without actual division, find whether the following rational numbers are terminating decimals or recurring decimals : (i) 13/45 (ii) −5/56 (iii) 7/125 (iv) −23/80 (v) −15/66. In case of terminating decimals, write their decimal expansions.

Rational Irrational Nos

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