Without actual division, show that each of the rational numbers given below is expressible as a repeating decimal : (i) 23/24 (ii) 79/30 (iii) 100/9 (iv) 205/27 (v) 461/60 (vi) 1003/112 (vii) 127/225 (viii) 219/440

Question

KnowledgeBoat · Accepted Answer

(i) The given rational number is . Its denominator is . Thus, the denominator of has at least one prime factor, namely 3, other than 2 and 5. ∴ is expressible as a repeating decimal. (ii) The given rational number is . Its denominator is . Thus, the denominator of has a prime factor, namely 3, other than 2 and 5. ∴ is expressible as a repeating decimal. (iii) The given rational number is . Its denominator is . Thus, the denominator of has at least one prime factor, namely 3, which is different from 2 and 5. ∴ is expressible as a repeating decimal. (iv) The given rational number is . Its denominator is . Thus, the denominator of has at least one prime factor, namely 3, which is different from 2 and 5. ∴ is expressible as a repeating decimal. (v) The given rational number is . Its denominator is . Thus, the denominator has at least one prime factor, namely 3, other than 2 and 5. ∴ is expressible as a repeating decimal. (vi) The given rational number is . Its denominator is . Thus, the denominator has at least one prime factor, namely 7, other than 2 and 5. ∴ is expressible as a repeating decimal. (vii) The given rational number is . Its denominator is . Thus, the denominator has at least one prime factor, namely 3, which is different from 2 and 5. ∴ is expressible as a repeating decimal. (viii) The given rational number is . Its denominator is . Thus, the denominator has a prime factor, namely 11, other than 2 and 5. ∴ is expressible as a repeating decimal.

Mathematics

Without actual division, show that each of the rational numbers given below is expressible as a repeating decimal : (i) 23/24 (ii) 79/30 (iii) 100/9 (iv) 205/27 (v) 461/60 (vi) 1003/112 (vii) 127/225 (viii) 219/440

Rational Numbers

Related Questions