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Add using the standard algorithm

The standard addition algorithm combines multi-digit whole numbers and finite decimals by aligning corresponding place values, adding from right to left, and regrouping when a place total reaches ten; trailing zeros may be used to preserve decimal alignment. The method expresses the composition of quantities through the base-ten system, and estimation or inverse subtraction can check reasonableness; it does not extend here to arbitrary-precision numbers, signed numbers, or algebraic expressions.

Detailed Explanation: Add using the standard algorithm

To add multi-digit whole numbers or decimals:

  1. Line up the place values. Line up the decimal points, then add trailing zeros if needed.
  2. Add from right to left.
  3. If a column totals 10 or more, write the ones digit and regroup the tens digit into the next column.
  4. Bring the decimal point straight down into the answer.

Example:

347.58326.70\begin{array}{r} 347.58\\ \phantom{3}26.70\\ \hline \end{array}

The zero in (26.70)(26.70) keeps the decimal places aligned.

  • Hundredths: (8+0=8)(8+0=8). Write 88.
  • Tenths: (5+7=12)(5+7=12). Write 22 in the tenths place and regroup 11 ten to the ones place.
  • Ones: (7+6+1=14)(7+6+1=14). Write 44 and regroup 11 ten to the tens place.
  • Tens: (4+2+1=7)(4+2+1=7). Write 77.
  • Hundreds: Bring down 33.

The decimal point goes straight down:

347.58326.70374.28\begin{array}{r} 347.58\\ \phantom{3}26.70\\ \hline 374.28 \end{array}

So, (347.58+26.70=374.28)(347.58+26.70=\boxed{374.28}).

Learn by doing: Add using the standard algorithm

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Addition - Whole Number 4 digit + 3 digit - Column, With Carry


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