Hi all ....

**r-soy** · Dec 24th 2009, 03:21 AM

Hi
In this question How I know 0,000001 = 10^-2
Is there a way ? Is there a way by Calculator ?

**dedust** · Dec 24th 2009, 03:32 AM

Originally Posted by r-soy

Hi
In this question How I know 0,000001 = 10^-2
Is there a way ? Is there a way by Calculator ?

this is wrong,..

$0,000001 = \frac{1}{100000} = 10^{-6}$ not $10^{-2}$

**r-soy** · Dec 24th 2009, 04:32 AM

sorry i mean 0,0001 = 10^-2

i can't undertand your way

Is there another way ?

**Raoh** · Dec 24th 2009, 04:39 AM

Originally Posted by r-soy

sorry i mean 0,0001 = 10^-2

i can't undertand your way

Is there another way ?

0,0001 = 10^-2 is wrong too.

**r-soy** · Dec 24th 2009, 04:51 AM

hhh i am confused

i mean 0,0001 = 100^-2

see the image and see the solving

**Shinichi** · Jan 1st 2010, 11:56 AM

Remember that $\log_a{b}=c \Longleftrightarrow\ a^{c} = b$ , with $\log_a{b}=c$ well defined.

What it's written in yor exercise is just the aplication of the above.

Thus, you know $\log_b{0,0001}=-2 \Longleftrightarrow\ b^{-2}=0,0001$ , but also know $0,0001=10^{-4}=(10^{2})^{-2}$ , because a propertie of powers says $(a^{b})^{c}=a^{bc}$ with $(a^{b})^{c}$ well defined.

Therefore, $b=100$

**HallsofIvy** · Jan 2nd 2010, 04:37 AM

Without logarithms, 0,0001 ("one ten thousandth") means 1/10000= 1/(10)(10)(10)(10)= 1/10^4= 10^(-4).

0,01= 1/100= 1/(10^2)= 10^(-2).

Easy way- count the number of "decimal places"= 0,0001 has four places so is 10^(-4), 0,01 has 2 places so is 10^(-2).

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