Question

When written in decimal form, which of the following will be a non-terminating, non-recurring number?
a.1 by 1/9
b.2 by 1/9
c.2'9
d9 by 1/2​

Answer 1

Given :- When written in decimal form, which of the following will be a non-terminating, non-recurring number ?

a) 1 by 1/9 => either it is 1/(1/9) or 1/9

b) 2 by 1/9 => 2/(1/9) or 2(1/9)

c) 2'9 => 2/9

d) 9 by 1/2 => 9/(1/2) or 9(1/2) .

Answer :-

we have to check prime factors of denominators of given fraction .

• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

so, checking given options we get,

a) 1/(1/9)

→ 1 * 9/1

→ 9/1

→ 9 = rational number .

or,

→ 1(1/9)

→ 10/9

→ Prime factors of denominator = 3 * 3 ≠ 2 or 5 => non - terminating number .

b) 2/(1/9)

→ 2 * 9/1

→ 18/1

→ 18 = rational number .

or,

→ 2(1/9)

→ 19/9

→ Prime factors of denominator = 3 * 3 ≠ 2 or 5 => non - terminating number .

c) (2/9)

→ Prime factors of denominator = 3 * 3 ≠ 2 or 5 => non - terminating number .

a) 9/(1/2)

→ 9 * 2/1

→ 18/1

→ 18 = rational number .

or,

→ 9(1/2)

→ 19/2

→ Prime factors of denominator = 2 => terminating number .

Learn more :-

(3) निम्न के स्थानीय मान लिखिये-

(अ)43.24

(स)884.20

(ब) 534.34

(द) 178.34

https://brainly.in/question/37666224

Answer 2

Answer:

91/2

option d

Step-by-step explanation: