Question

decimal expansion of which of following is non terminating a)2/5 b)3/6 c)3/11 d)137/25 HELP ME I AM TOTALLY STUCK​

Answer 1

Answer:

c) 3/11

Step-by-step explanation:

We know that a number terminates if its denominator is of the form 2^m × 5^n where m and n are positive integers

so now let's check if they are in line for this.....

also, do know that to find when the decimals terminate look into the greatest power between 2 and 5

if m<n then it will terminate after n digits and if m>n then it will terminate after m digits(Just for your information)

a)2/5 = 2/(2⁰ × 5¹), is of the form 2^m × 5^n, so it is terminating (we know when the power is 0 the whole value becomes 1) and will terminate after 1 digit.

b)3/6 = 1/2 (always remember to make them in the simplest form)

1/2 = 1/(2¹ × 5⁰) is of the form 2^m × 5^n, so it is terminating and will terminate after 1 digits

c)3/11 = 3/(2⁰ × 5⁰ × 11) is not of the form 2^m × 5^n, so it is non terminating.

also,

d)137/25 = 137/(2⁰ × 5²) is of the form 2^m × 5^n, so it is terminating and will terminate after 2 digits.

So 3/11 is the decimal expansion, which is non terminating

Hope you understood it........All the best.

Answer 2

Answer:

3/11 is the answer bro. . . .

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