You have compared tenths and hundredths and you can read thousandths. Comparing works the same way at any size: the biggest places decide first.
Key idea
Line up the decimal points (or write both numbers with the same number of decimal places). Then compare place by place from the left. The first place where the digits differ decides.
Why it works
A tenth is bigger than any number of hundredths or thousandths that fit in the places after it: even $0.099$ is less than $0.1$. So the tenths digit matters more than everything to its right. Writing zeros at the end, like $0.5 = 0.500$, does not change a value, and it lets you compare like whole numbers: 500 thousandths against 125 thousandths.
Worked examples
Worked example: Different numbers of digits
Compare $0.125$ and $0.5$.
- Write both with three places: $0.125$ and $0.500$.
- Tenths: 1 and 5. They differ, and $1 < 5$.
Answer: $0.125 < 0.5$
Worked example: Same tenths
Compare $2.09$ and $2.1$.
- Ones: both 2.
- Tenths: 0 and 1. $0 < 1$.
Answer: $2.09 < 2.1$
Worked example: Equal values
Compare $3.40$ and $3.4$.
- Write $3.4$ as $3.40$.
- Every place matches.
Answer: $3.40 = 3.4$
Common mistake
Thinking $0.125 > 0.5$ because 125 is greater than 5. The digits are in different places: the 5 is 5 tenths, but the 1 is only 1 tenth. Check: give both the same number of decimal places, $0.125$ and $0.500$, then compare.