Solving for Inches in an Angstrom

[Drakkith]

Homework Statement

How many inches are in an angstrom, given that 1 angstrom = 10^-8 cm.

Homework Equations

1 angstrom = 10^-8 cm
1 inch = 2.54 cm

The Attempt at a Solution

Ok, I convert 1 angstrom to 10^-8 cm, then divide by 2.54. This gives me 3.94 x 10^-8, but the book says it's actually 3.94 x 10^-9. What did I do wrong with the exponents? Is 10^-8 the same as 10 x 10^-8?

 

[SHISHKABOB]

no it's not, 10 is 10¹, so 10 x 10^-8 is (10¹)(10^-8) which is 10^1-8 which is 10^-7

btw: I really hate angstroms ;_; they make life a pain in the butt because of things like this

 

[Drakkith]

So is 10^-8 = 1x10^-8?

 

[SHISHKABOB]

yeah, you're multiplying it by 1, A = 1*A

 

[Drakkith]

I don't follow you. Isn't 10^-8 equal to 0.0000001 while 1x10^-8 equal to 0.00000001? (6 zeros in the first, 7 in the second)

 

[SHISHKABOB]

I plugged 10^-8 into my calculator and got 0.00000001 which has six zeros

I did the same with 1x10^8- and got 0.00000001 as well

 

[Drakkith]

Both those have 7 zeros.

 

[SHISHKABOB]

whoops you're right

but still, they're the same

1*A = A

and so if A = 10^-8, then 1*10^-8 = 10^-8
remember that a^b = \frac{1}{a^{-b}}

so in our case we have 10^-8 = \frac{1}{10^{8}}

so then 1(10^-8) = \frac{1}{10^{8}}

 

[Drakkith]

Ok, from wikipedia: In the base ten (decimal) number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 10^3 = 1000 and 10^−4 = 0.0001.

So 10^-8 = 0.00000001, aka 1x10^-8.
Now it makes sense.