Compare, add and subtract decimals by matching units

Comparing only 8 and 12 in 0.8 and 0.12 mixes units. Eight counts tenths; twelve counts hundredths. Rewrite 0.8 as 0.80 to read both in hundredths.

Since 80/100 exceeds 12/100, 0.8 is greater. Compare corresponding place values, not string lengths or the integers after the decimal point. The equivalence of 0.80 and 0.8 makes this possible.

For 0.6+0.25, use 60/100+25/100=85/100, or 0.85. Aligning decimal points in a column calculation aligns tenths with tenths and hundredths with hundredths; it is not just neat formatting.

For 1.20−0.35 there are initially no hundredths to remove five from. Open a tenth into ten hundredths and, when needed, a whole into ten tenths. Whole-number unbundling extends to smaller places. The result is 0.85.

Adding 0.6 L of water to 0.25 L uses the same litre unit. Aligning digits does not make it meaningful to add metres to litres. Name the measured quantity as well as the place values.