# Choose the Correct Alternative Answer for the Question Given Below. - Algebra

MCQ

Choose the correct alternative answer for the question given below.

Decimal expansion of which of the following is non-terminating recurring ?

#### Options

• 2/5

• 3/16

• 3/11

• 137/25

#### Solution

1) Since ,5 = 2^0 xx 5^1 , which is in the form of 2^m xx 5^n, where m and n are non - negative integers.

So, the decimal expansion of 2/5 is terminating.

2) Since , 16 = 2^4 xx 5^0, which in the form of 2^m xx 5^n , where m and n are non - negative integers.

So, the decimal expansion of 3/16 is terminating.

3) Since , 11 = 2^0 xx 5^0 xx 11^1, which is not in the form of 2^m xx 5^n, where m and n are non - negative integers.

So, the decimal expansion of 3/11 is non - terminatingrecurring.

4) Since , 25 = 2^0 xx 5^2 , which is in the form of 2^m xx 5^n, where m and n are non - negative integers.

So, the decimal expansion of 137/25 is terminating.

Concept: Properties of Real Numbers
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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 2 Real Numbers
Problem Set 2 | Q 1.03 | Page 34