# Solution - Revisiting Rational Numbers and Their Decimal Expansions

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ConceptRevisiting Rational Numbers and Their Decimal Expansions

#### Question

Write down the decimal expansions of those rational numbers  which have terminating decimal expansions.

(a) 13/3125

(b) 17/8

(c)15/1600

(d)23/(2^2

(e)6/15

(f)35/50

#### Solution

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

(i)13/3125

(ii) 17/8

(iii) 64/455

(iv) 15/1600

(v) 29/343

(vi) 23/(2^3

(vii) 129/(2^2

(viii) 6/15

(ix) 35/50

(x) 77/210

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The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form p /q what can you say about the prime factors of q?

(1) 43.123456789

(2) 0.120120012000120000. . .

(3) 43.bar(123456789)

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#### Reference Material

Solution for concept: Revisiting Rational Numbers and Their Decimal Expansions. For the course 8th-10th CBSE
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