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Subtract decimals

Decimal subtraction represents finding the difference between nonnegative decimal quantities by decomposing whole units into tenths, hundredths, and thousandths as needed. Place-value columns are aligned by the decimal point, and zeros may be appended to equivalent decimals without changing their value; estimation and number-line reasoning help determine whether a result is reasonable and prevent treating digits as whole-number strings. This scope concerns finite decimals, typically through thousandths, rather than repeating decimals or generalized operations with signed rational numbers.

Detailed Explanation: Subtract decimals

To subtract decimals, line up the numbers by their decimal points. Then subtract digits in each place-value column, starting from the right.

Example: Find (5.2−3.78)(5.2-3.78).

First, write the numbers with aligned decimal points. Add a zero to (5.2)(5.2) so both numbers have hundredths:

5.20−3.78\begin{array}{r} 5.20\\ - 3.78\\ \hline \end{array}

Estimate first: (5.2−3.8)(5.2-3.8) is about (1.4)(1.4), so the answer should be close to (1.4)(1.4).

Now subtract from right to left:

  1. In the hundredths column, (0−8)(0-8) is not possible. Regroup 11 tenth as (10)(10) hundredths. This leaves 11 tenth and gives (10)(10) hundredths:
10−8=2 10-8=2
  1. In the tenths column, (1−7)(1-7) is not possible. Regroup 11 whole as (10)(10) tenths. This leaves 44 ones:
11−7=4 11-7=4
  1. In the ones column:
4−3=1 4-3=1

The decimal point stays in the same column:

5.20−3.781.42\begin{array}{r} 5.20\\ - 3.78\\ \hline 1.42 \end{array}

Therefore,

5.2−3.78=1.42\boxed{5.2-3.78=1.42}

The answer is reasonable because (1.42)(1.42) is close to the estimate of (1.4)(1.4).

Learn by doing: Subtract decimals

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    Subtraction - Decimal Tenths (Column)

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