Lining Up the Places

Tenths can only be added to tenths, and hundredths to hundredths.

It is not about the point

People say "line up the decimal point". What they mean is line up the places.

Fill the gaps

To add 3.4 and 1.25, write 3.40. The extra 0 changes nothing and makes the places match.

The same rule as Grade 1

You could never add a ten to a one. This is that rule, one place further right.

Aligning points aligns units

Writing 3.4 + 12.75 with the decimal points in a column puts tenths above tenths and ones above ones. That alignment is the entire justification for column addition — like units combine, unlike units do not. Aligning the right-hand edges instead would add tenths to hundredths.

Pad the shorter number

Write 3.4 as 3.40 so both numbers show hundredths. The value is unchanged and every column is now filled, which removes any temptation to shift digits to fill a gap. This is exactly the common-denominator step from fractions.

Whole numbers have an invisible point

12 is 12.00, with the point sitting just after the 2. When adding 12 to 3.47, write 12.00 so the alignment is visible. Forgetting that a whole number has a decimal point is a common source of misaligned working.

Estimate with whole numbers

3.4 + 12.75 is roughly 3 + 13 = 16. The exact answer, 16.15, fits. Misalignment errors are large — often off by a factor of ten — so even a crude whole-number estimate exposes them at once.