Problem Solving

1/[10^(n+1)] < 0.00625 < 1/[10^(n+1)]

what is the value of n?

I suspect that the correct equation is 1/[10^(n+1)] < 0.00625 < 1/[10^n]. So I'll try and solve it like this. Let's devise a rule here:
1/10 = 0.1
1/(10^2) = 0.01
1/(10^3) = 0.001
From this you can tell that, for 1/(10^n), you get a number that has (n-1) "zeros" after the point. Now, 0.00625 is greater than 0.00001, which will therefore be 1/(10^5) (since you have 4 "zeros" after the point). The immediately greater number will be 1/(10^4), so you get that:
1/(10^5) < 0.00625 < 1/(10^4). So n = 4.

DanaJ wrote:I suspect that the correct equation is 1/[10^(n+1)] < 0.00625 < 1/[10^n]. So I'll try and solve it like this. Let's devise a rule here:
1/10 = 0.1
1/(10^2) = 0.01
1/(10^3) = 0.001
From this you can tell that, for 1/(10^n), you get a number that has (n-1) "zeros" after the point. Now, 0.00625 is greater than 0.00001, which will therefore be 1/(10^5) (since you have 4 "zeros" after the point). The immediately greater number will be 1/(10^4), so you get that:
1/(10^5) < 0.00625 < 1/(10^4). So n = 4.

Dear DanaJ,

If the question is 1/[10^(n+1)] < 0.00625 < 1/[10^n], then the value of n will be 2 and not 4.

If n is 4, then 1/10^4 = 0.0001 and definitely 0.00625 is greater than this.

The value of n must be 2 here and not 4.

Let's look at the solution

Given 1/[10^(n+1)] < 0.00625 < 1/[10^n]

i.e 1/[10^(n+1)] < 625/100000 < 1/[10^n]

i.e 1/[10^(n+1)] < 1/160 < 1/[10^n]

From this we can conclude that, 10^n < 160 < 10^(n+1) (If a and b are non-positive and 1/a < 1/b, then a > b)

So it is clear that the value of n is 2.

Oops, sorry. You are right...I guess it's still to early in the morning for me :)