Decimals - Addition of Numbers with Decimals

Place Value Chart: Decimals expand the standard place value system. To the left of the decimal point, we have ones, tens, and hundreds. To the right, we have tenths ($\frac{1}{10}$), hundredths ($\frac{1}{100}$), and thousandths ($\frac{1}{1000}$). Visualize a grid where the decimal point acts as a fixed wall separating the whole numbers from the fractional parts.

Alignment of Decimal Points: The most critical rule is to align the decimal points vertically when writing the numbers one below the other. Imagine a straight vertical line or 'spine' passing through every decimal point in the problem; this ensures that tenths are added to tenths and ones are added to ones.

Converting to Like Decimals: Before adding, convert unlike decimals into 'like decimals' by adding placeholder zeros at the end. For example, if adding $5.2$ and $3.14$, visualize $5.2$ becoming $5.20$ so that both numbers have two digits after the decimal point.

Column-wise Addition: Addition starts from the rightmost column (the smallest place value) and moves to the left. Just like whole number addition, you add each digit in its specific lane: thousandths, then hundredths, then tenths, then ones, and so on.

Regrouping (Carrying Over): If the sum in any column is $10$ or more, the 'tens' part of that sum is carried over to the next column on the left. For example, if the tenths column adds up to $13$, you write $3$ in the tenths place and carry $1$ over to the ones place.

Decimal Placement in the Result: The decimal point in the final sum must be placed directly beneath the vertical line of decimal points from the numbers being added. It does not move left or right; it remains in its designated 'lane'.

Empty Spaces: In the place value columns, empty spaces should be treated as zeros. If a whole number like $7$ is added to a decimal like $0.5$, visualize $7$ as $7.0$ to keep the alignment clear.