Finding a and n when 7 × 10^6 ÷ a × 10^n = 8.75 × 10^9

[abey_27]

7 × 10^6 divided by a × 10^n is equal to 8.75 × 10^9

a is greater or equal to 1 but less than 10. n is an integer.

Find the value of a and the value of n.
I do not really understand how to separate the a and n, and thus find a value for each of them. Some help would be highly appreciated.


thanks integral, but how exactly does that help??

Remember:

$$\frac {a b} {c d} = \frac a c . \frac b d$$

 

[Ertosthnes]

It's easier if you don't think about the algebra. Set up the equation like this:

$$\frac{7*10^6}{a*10^n}$$=$$\frac{7}{8}$$*10^10

Hopefully it's obvious that 8.75*10^9 = (7/8)*10^10.

From there you can just sort of see the numbers that will work.

 

[Integral]

Your problem is

$$\frac {7 x 10^6} {a x 10^n} = 8.75 x 10^9$$

You can't see that this is the same form as the fraction in my first post?