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Comparing decimals uses the same left-to-right, place-by-place strategy as comparing whole numbers, but students must resist the temptation to judge by the number of digits. 0.5 > 0.38 because 5 tenths > 3 tenths, even though 38 > 5 as whole numbers. Appending trailing zeros (rewriting 0.5 as 0.50) can make comparisons clearer by aligning place values. Students should be able to compare any two decimals through thousandths using <, >, and =, and order sets of decimals from least to greatest or greatest to least.
Use place-value charts side by side, comparing digit by digit from left to right. 10x10 grids (hundredths grids) make the comparison visual. Practice with carefully chosen pairs: same whole-number part but different decimal parts, different lengths, trailing zeros. Always connect back to the meaning: "5 tenths versus 3 tenths and 8 hundredths."
You've learned how the decimal place-value system works — tenths, hundredths, thousandths extending the whole-number system to the right of the decimal point — and you know how to read and write decimals. You've also compared whole numbers before. Comparing decimals uses the exact same strategy as comparing whole numbers: start from the leftmost digit and work right until you find a place where the digits differ.
The algorithm is: align the decimal points, then compare digit by digit from left to right. For 0.5 and 0.38, the tenths digits are 5 vs. 3. Since 5 > 3, we know 0.5 > 0.38 immediately — the hundredths digit of 0.38 is irrelevant because the comparison was already decided at the tenths place. A useful technique is appending trailing zeros: rewrite 0.5 as 0.50 so both numbers have digits in the same place-value positions. Now the comparison reads "50 hundredths versus 38 hundredths," which looks exactly like comparing 50 and 38 as whole numbers. The trailing zero doesn't change the value, but it makes the alignment visible and explicit.
The most seductive mistake is judging by digit count: "0.125 has three decimal places, so it must be bigger than 0.9 which has only one." This reverses the truth. Rewrite 0.9 as 0.900 — that's 900 thousandths versus 125 thousandths. The connection to your prerequisite on fractions and decimals makes this concrete: 0.9 = 9/10 and 0.125 = 125/1000. Converting to a common denominator (thousandths) gives 900/1000 vs. 125/1000 — 0.9 is clearly larger. The number of digits after the decimal point tells you nothing about size on its own; only the place-value of the leading differing digit matters.
Ordering a set of decimals from least to greatest follows the same logic extended to multiple numbers: compare whole-number parts first (any decimal ≥ 1 is greater than any decimal < 1), then tenths, then hundredths, and so on until all ties are broken. Numbers that differ only in trailing zeros are equal (0.50 = 0.500 = 0.5). Fluency here supports every operation with decimals that follows — adding, subtracting, rounding, multiplying — because all of them depend on understanding what the digits in each place actually represent.