| Directions: Q. 21 to 25 |
| Decimal Expansion |
| Decimal form of rational numbers can be classified into two types. |
| Let a be a rational number whose decimal expansion terminates. Then a can be expressed in the form \[\frac{p}{q}\], where p and q are co-prime and the prime factorisation of q is of the form \[{{2}^{n}}\,5{{\,}^{m}}\], where n, m are non-negative integers and vice-versa. |
| Let \[a=\frac{p}{q}\]be a rational number, such that the prime factorisation of q is not of the form \[{{2}^{n}}{{5}^{m}}\], where n and m are non-negative integers. Then a has a non-terminating repeating decimal expansion. |
| Based on the above information answer the following questions. |
A) 8/15
B) 51/150
C) \[15/400\]
D) \[129/\left( {{2}^{2}}\times {{5}^{2}}\times {{7}^{2}} \right)\]
Correct Answer: C
Solution :
| The simplest form of are the options can be written as |
| \[\frac{8}{15}=\frac{{{2}^{3}}}{3\times 5}\] |
| \[\frac{51}{150}=\frac{51}{2\times 3\times {{5}^{2}}}\] |
| \[\frac{15}{400}=\frac{3\times 5}{{{2}^{4}}\times {{5}^{2}}}\] |
| \[=\frac{129}{{{2}^{2}}\times {{5}^{2}}\times {{7}^{2}}}\] |
| Only [c] has denominator in the form of \[{{2}^{n}}{{5}^{m}}\] |
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