posted by jack .
How Can I Find The Value Of (10 ^ -0.1)
(Without Using Calculator)
That's not possible. But 10^-1 is. You move your decimal to the left for negative exponents and you move your decimal to the right for positive exponents. If you had a value of 1 X 10^-2 for example you would move your decimal two places to the left which would equal .01 in decimal format. If you are in fact referring to scientific notation.
So you want 1 divided by the tenth root of 10.
In the days before calculators, we would now have to rely on log tables.
We would have proceeded something like this
let x = 10^(-1/10)
logx = log [10^(-1/10) ]
= (-1/10) log10
= -1/10 or -.1
= -1 + .9
we would then find the "antilog of .9 from tables to get 7.9433
the -1 would tell us to move the decimal one place to the left to get
10^ -.1 as .79433
log tables were only valid for positive logs, so if you had a negative, it was necessary to split it up into an integer + a positive decimal
in our -1 + .9
the -1 was called the characteristic, and the .9 is called the mantissa.
The mantissa always had to be positive.
so if we had something like
logx = -3.35 it had to be changed to
log = -4 + .65
You are sooo fortunate to have calculators