Question

Let the number 0.000000....001 which has 2019 zeros after decimal point. Then which of the following numbers is the greatest
A) 10000+x
B) 10000*x
C) 10000/x
D) 1/x to the power 2

Answer 1

Answer:

Option (D) is correct; 1/x² is the greatest number.

Explanation:

Here, x = 0.000 ... 0001 , which has 2019 zeroes after the decimal

= 10⁻²⁰²⁰

(A)

Here, 10000 + x

= 10000.000 ... 0001 , which has 2019 zeroes after the decimal

< 10⁵

(B)

Here, 10000 * x

= 10000 * 10⁻²⁰²⁰

= 10⁴ * 10⁻²⁰²⁰

= 10⁻²⁰¹⁶

(C)

Here, 10000/x

= 10⁴ / 10⁻²⁰²⁰

= 10⁴ * 10²⁰²⁰

= 10²⁰²⁴

(D)

Here, 1/x²

= 1/(10⁻²⁰²⁰)²

= 1/10⁻⁴⁰⁴⁰

= 10⁴⁰⁴⁰

Thus we see that 10⁴⁰⁴⁰ is the greatest number of all and therefore 1/x² is the greatest.