Posted by **jack** on Sunday, August 28, 2011 at 5:50am.

How Can I Find The Value Of (10 ^ -0.1)

(Without Using Calculator)

- math -
**Davis**, Sunday, August 28, 2011 at 5:58am
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.

- math -
**Reiny**, Sunday, August 28, 2011 at 8:51am
10^-.1

= 1/10^.1

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)(1)

= -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

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