Express the sum as a common fraction: $.1 + .02 + .003 + .0004 + .00005.$
The five decimals sum to $0.12345$, which as a fraction is $\frac{12,\!345}{100,\!000}$.  Since $100,\!000=2^5\cdot 5^5$, we only have to cancel factors of 2 or 5 from $12,\!345$.  Since $12,\!345$ is odd, it has no factors of 2.  Dividing by 5, we find that $\dfrac{12,\!345}{100,\!000}=\boxed{\dfrac{2469}{20,\!000}}$.
\dfrac{2469}{20000}
Level 2
Number Theory
Problem: Express the sum as a common fraction: $.1 + .02 + .003 + .0004 + .00005.$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the sum of the decimals, convert each decimal to a fraction. 

0.1 can be expressed as 1/10. 
0.02 can be expressed as 2/100, which simplifies to 1/50. 
0.003 can be expressed as 3/1000. 
0.0004 can be expressed as 4/10000, which simplifies to 1/2500. 
0.00005 can be expressed as 5/100000, which simplifies to 1/20000. 

Next, find a common denominator for all fractions. The least common multiple of the denominators 10, 50, 1000, 10000, and 20000 is 20000. 

Convert each fraction to have this common denominator: 
1/10 = 2000/20000, 
1/50 = 400/20000, 
3/1000 = 60/20000, 
1/2500 = 8/20000, 
1/20000 = 1/20000. 

Now, sum the numerators: 
2000 + 400 + 60 + 8 + 1 = 2469. 

Thus, the sum of the fractions is 2469/20000. 

The final answer is 2469/20000.<|END_OF_LATENT|> The final answer is $\dfrac{2469}{20000}$.