Decimals - Subtraction of Decimals

Alignment of Decimal Points: When subtracting decimals, the most crucial step is to align the decimal points of both numbers vertically in a straight column. This ensures that digits of the same place value, such as tenths under tenths and units under units, are correctly positioned for subtraction. Imagine a vertical dotted line passing through the decimal points of both numbers and the result.

Converting to Like Decimals: Before subtracting, ensure both numbers have the same number of decimal places. If they do not, add placeholder zeros (0) to the right of the decimal part of the number with fewer places. For example, if you have $5.8$ and $2.15$, write $5.8$ as $5.80$. Visually, this creates a complete rectangular grid where every digit has a corresponding partner above or below it.

Place Value Integrity: Subtract digits in each column starting from the rightmost place (e.g., thousandths, then hundredths, then tenths) and moving to the left. Just like in whole number subtraction, the value of each column is fixed: the first digit to the right of the point is the tenths ($\frac{1}{10}$), the second is the hundredths ($\frac{1}{100}$), and so on.

Regrouping or Borrowing: If a digit in the top number (minuend) is smaller than the digit in the bottom number (subtrahend) in the same column, you must 'borrow' or regroup from the column to the immediate left. For example, borrowing $1$ from the tenths place gives you $10$ in the hundredths place. Visually, this is represented by crossing out the digit to the left and reducing its value by $1$ while adding $10$ to the current digit.

Placement of the Decimal Point in the Result: The decimal point in the final difference must be placed exactly in the same vertical line as the decimal points in the numbers being subtracted. It serves as the anchor that separates the whole number part from the fractional part of the answer.

Verification through Addition: You can verify your subtraction result by adding the difference to the subtrahend. If the sum equals the original minuend, the calculation is correct. This is expressed as $\text{Difference} + \text{Subtrahend} = \text{Minuend}$.