# Which one of the following is a correct statement? (a) Decimal expansion of a rational number is terminating

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Which one of the following is a correct statement?

(a) Decimal expansion of a rational number is terminating

(b) Decimal expansion of a rational number is non-terminating

(c) Decimal expansion of an irrational number is terminating

(d) Decimal expansion of an irrational number is non-terminating and non-repeating

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The following steps for successive magnification to visualise 2.665 are:

(a) We observe that 2.665 is located somewhere between 2 and 3 on the number line. So,

let us look at the portion of the number line between 2 and 3.

(b) We divide this portion into 10 equal parts and mark each point of division. The first

mark to the right of 2 will represent 2.1, the next 2.2 and soon. Again we observe that

2.665 lies between 2.6 and 2.7.

(c) We mark these points Aand A2 respectively. The first mark on the right side of A1 , will

represent 2.61, the number 2.62, and soon. We observe 2.665 lies between 2.66 and 2.67.

(d) Let us mark 2.66 as Band 2.67 as B2 . Again divide the B1B2 into ten equal parts. The

first mark on the right side of B1will represent 2.661. Then next 2.662, and so on.

Clearly, fifth point will represent 2.665.