Write the characteristic of each of the following

log 0.00257

Characteristic: In a scientific number, the power of 10 determines the characteristic.

Let N = 0.00257

Divide N by 10⁵ to remove decimal, we get

Multiply and Divide N by 100, we get

Thus, scientific notation 0.00257 = 2.57 × 10^–3

Consider,

log 0.00257 = log (2.57 × 10^–3 )

= log 2.57 + log 10^–3

(since, log (a×b) = log a + log b)

= log 2.57 + (–3)

(since, log 10ⁿ = n)

Thus characteristic of log 0.00257 is –3