Test Index

Logarithms

Question : 23 of 85

Marks: +1, -0

\log 2=0.3010,

2^{-37}

is :

Solution:

Concept:

For a number less than 1, the position of the first significant digit after the decimal is given by

|\text{characteristic}|

of its logarithm (base 10).

Explanation:

Compute

\log_{10}(2^{-37}) = -37 \times \log_{10}2 = -37 \times 0.3010 = -11.137

Write

-11.137 = -12 + 0.863

. Here the characteristic is

-12

and mantissa

0.863

The number of zeros after the decimal before the first non-zero digit is

12 - 1 = 11

Thus the first significant digit appears at the

12

th decimal place.

Answer:

12 th

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