What is:
3.4 + 0.56?
A learner who lines up the final digits may write 3.40 over 0.56 by accident and get the right structure.
Another may write 3.4 over 0.56 with the 4 above the 6 because the numbers “end together”.
The second layout mixes tenths with hundredths.
Decimal algorithms work when equal place-value units are aligned, not when digit strings are made to look neat.
Write 3.4 as 3.40.
Then:
3.40 + 0.56 = 3.96.
The current Singapore Primary Mathematics syllabus includes, in Primary 4, adding and subtracting decimals up to 2 decimal places. That arithmetic sits directly on the place-value work that introduces tenths, hundredths and thousandths.
The decimal point is an alignment marker
In vertical calculation, decimal points line up because ones must align with ones, tenths with tenths and hundredths with hundredths.
For example:
12.35 + 4.70.
Align:
12.35
+ 4.70
Hundredths: 5 + 0 = 5.
Tenths: 3 + 7 = 10 tenths = 1 whole.
Ones: 2 + 4 + 1 = 7.
Tens: 1.
Answer: 17.05.
The carried value is one whole because 10 tenths make 1 whole.
Equivalent notation makes alignment visible
3.4 = 3.40.
0.7 = 0.70.
5 = 5.00.
Adding trailing zeros does not change value. It expresses the quantity in finer decimal units.
This is especially useful when one addend has fewer decimal places than another.
Estimate before exact decimal calculation
3.4 + 0.56 is about:
3.4 + 0.6 ≈ 4.0.
Exact answer 3.96 fits the estimate.
An answer such as 39.6 should be rejected immediately as a place-value error.
Subtraction requires the same place-value discipline
Consider:
5.2 − 1.78.
Rename 5.2 as 5.20.
Now subtract aligned hundredths, tenths and ones.
5.20 − 1.78 = 3.42.
The zero in 5.20 is useful because it makes the hundredths place explicit before regrouping.
Regrouping crosses the decimal point naturally
In 5.20 − 1.78, the hundredths place needs 0 − 8.
Rename one tenth as 10 hundredths.
The tenths place decreases by one tenth.
If needed, one whole can be renamed as 10 tenths.
This is the same base-ten exchange used in whole-number subtraction.
Decimal regrouping is not a new kind of borrowing. It is the same base-ten renaming system extended below one.
Worked example: 7.35 + 2.8
Rename 2.8 as 2.80.
7.35 + 2.80 = 10.15.
Estimate:
7.4 + 2.8 ≈ 10.2.
The exact answer is plausible.
Worked example: 10 − 3.47
Write 10 as 10.00.
Then:
10.00 − 3.47 = 6.53.
The equivalent notation does not change ten. It exposes tenths and hundredths so the subtraction can be represented consistently.
Common misconception 1: line up the last digits
This can align different units accidentally.
Repair: line up decimal points because that aligns place values.
Common misconception 2: ignore zeros because they mean nothing
0.5 = 0.50, but writing the second form can be essential for showing hundredths during subtraction.
The zero may preserve value while still carrying representational purpose.
Common misconception 3: more decimal places means larger answer
2.75 is not automatically larger than 3.1 because it has more digits.
Compare place value from the left.
Common misconception 4: decimal addition changes the decimal point position
The decimal point remains aligned with the ones–tenths boundary.
It does not move because an answer grew beyond 10 or shrank below 1.
A diagnostic ladder
- Can the learner name tenths and hundredths place values?
- Can the learner explain 3.4 = 3.40?
- Can the learner align decimals by place value?
- Can the learner add without regrouping?
- Can the learner add with regrouping across the decimal point?
- Can the learner subtract using equivalent notation such as 5.20?
- Can the learner estimate the result before exact work?
- Can the learner reject factor-of-ten errors?
- Can the learner explain the unit of every regrouped amount?
How this fits Singapore Primary 4 Mathematics
The current MOE Primary Mathematics syllabus includes adding and subtracting decimals up to 2 decimal places in Primary 4. This sits beside decimal place-value study up to thousandths and therefore depends on learners distinguishing value from appearance.
The deeper lesson
Whole-number algorithms and decimal algorithms are one system.
Both require equal units to align.
Both regroup ten smaller units as one larger unit.
The decimal point simply marks where the place-value system crosses below one whole.
Align values, not digits. Once the units align, the arithmetic becomes ordinary base-ten calculation again.
Final thought
3.4 and 0.56 look uneven as strings.
As place-value quantities, they fit perfectly.
Three ones, four tenths, zero hundredths.
Zero ones, five tenths, six hundredths.
That is the alignment the algorithm is trying to preserve.