Question

find a positive number smaller than 1/21 to the power 1000.justify.
step by step explanation please please​

Answer 1

Explanation:

We have to compare the numbers \frac{1}{2^{1000}}\text{and}\frac{1}{2^{1001}}

2

1000

1

and

2

1001

1

The numerator of both the numbers is same. Hence, the number which have greater denominator is smaller number.

In the denominator, the base is same as 2. Hence, the more is the exponent (power) the greater is the number.

1001 > 1000

Hence, we can say that

2^{1001} > 2^{1000}2

1001

>2

1000

Therefore, the number with exponent 1000 is greater than the number with exponent 1001 on 2.

Hence, we can say that

\frac{1}{2^{1000}} > \frac{1}{2^{1001}}

2

1000

1

>

2

1001

1