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.
Find the value of a and the value of n.
(7X10^6)/(aX10^n) = 8.75X10^9 where a>=1 and a<10.
7X10^6 = aX10^n X 8.75X10^9
1/8.75 = aX10^(n+9-6)
0.8 = aX10^(n+3)
8/10 = aX10^(n+3)
8 = aX10^(n+3) X 10^1
8 = aX10^(n+3+1)
8 = aX10^(n+4)
a = 8/[10^(n+4)]
a>=1
8/[10^(n+4)]>=1
8>=10^(n+4)
log8>=log10^(n+4)
log8>=(n+4)log10
log8>=(n+4)(1) (since log10 =1)
log8>=n+4
log8-4>=n
-3.096910013>=n
or
a<10
8/[10^(n+4)]<10
8<10X10^(n+4)
8<10^(n+4+1)
8<10^(n+5)
log8<log10^(n+5)
log8<(n+5)log10
log8<(n+5)(1) (since log10 = 1)
log8<n+5
log8-5<n
0.4771212547<n
(I am not sure if the above solution is correct. It seems too involved. I feel that there might be an easier solution. I sure would like to know what it is. Cheers Abey.
I think i have the correct solution now:
working through it again...
7 x 10^6 = 8.75 x 10^9
a x 10^n
multiply through by a x 10^n, so you get:
7 x 10^6 = a x 10^n
8.75 x 10^9
Simplifying, 0.0008 = a x 10^n
0.0008 is the same as 8 x 10^-4
So a=8 and n = -4