Why does lining up decimal points matter when adding or subtracting?

The decimal point marks where whole-number places end and fractional places begin. Each column has a place-value meaning: ones, tenths, hundredths, and so on. Lining up the points puts matching places in the same columns, so you add or subtract tenths from tenths and hundredths from hundredths—not, for example, a tenth from a hundredth. The standard written method aligns decimal points, uses zeros as placeholders where helpful, and places the result’s decimal point in line with the others. [S1]

Here is addition worked column by column:

  23.50
+ 41.38
-------
  64.88

The 5 in 23.50 means 5 tenths; the 3 in 41.38 means 3 tenths. Those digits belong in the same column. The zero in 23.50 makes its hundredths column visible, matching the two decimal places in 41.38. It does not change the amount: 23.5 and 23.50 are equal.

Write the numbers one under the other with their decimal points aligned. If a number has fewer digits after the decimal point, add zeros on its right until the columns are clear. These are placeholder zeros: they show an empty place without changing the number’s value. For instance, rewrite 23.5 as 23.50 before adding 41.38; this is the same kind of alignment shown in the source example. [S1]

For example, align 6.4 and 2.17 by writing 6.4 as 6.40:

  6.40
+ 2.17
------

Now the hundredths, tenths, and ones columns are clear. Add from right to left as you would with whole numbers, carrying when needed. The setup shows how to align the values; the sum is 8.57.

Yes. Align the decimal points for subtraction too, and use a placeholder zero if one number has fewer decimal places. For example, to subtract 3.6 from 8.25, write 3.6 as 3.60:

  8.25
- 3.60
------
  4.65

The zero places 3.6’s value in the hundredths column as 3.60. It doesn’t mean the number is larger; it simply makes the columns easy to compare. The tenths digits line up (2 and 6), as do the hundredths digits (5 and 0). The answer’s decimal point stays directly beneath the points in the numbers. [S1]

If you subtract mentally, you may use a different method, but the written column method still depends on keeping matching place values together.

First check the setup, before redoing the arithmetic: are the decimal points in one vertical line? Do the digits in each column represent the same place value? Did you add any needed placeholder zeros to the right of a decimal number? Finally, check that the answer’s decimal point is in line with the others. [S1]

For a quick example, if you wrote 4.7 under 12.35 with the 7 under the 5, the columns would be mismatched. Write 4.7 as 4.70, then align the points:

 12.35
  4.70

This is an alignment check, not proof that every arithmetic step is correct. The guidance explains the setup and place-value alignment; it does not verify a particular learner’s work or establish a separate mental-math method. When practicing, estimate whether the result should be larger or smaller than the starting amount as an additional sense check.