We compare decimals place-by-place — the same principle as when comparing whole numbers. I also show a neat trick: you can make both decimals to have the same number of decimal digits for easier comparing. Lastly, if the decimals are particularly tricky to compare, use a place value chart.
Decimal place value — 6th grade video lesson
Long division with decimals, plus fractions to decimals — video lesson
Math Mammoth Fractions & Decimals 3 — self-teaching worktext