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Subtract decimals

Subtracting decimals involves finding the difference between nonnegative numbers expressed in tenths, hundredths, and thousandths, using place value to align decimal points and recognizing equivalent forms such as 3.4 and 3.400. The reasoning includes regrouping across decimal places, including across zeros, and connects the written method to base-ten or number-line representations and addition as an inverse relationship. This understanding is limited to nonnegative decimals through thousandths, not negative decimals or more advanced generalizations.

Detailed Explanation: Subtract decimals

To subtract decimals, line up the decimal points. This makes sure that ones are under ones, tenths are under tenths, hundredths are under hundredths, and thousandths are under thousandths. You can add zeros because they do not change a number: 5=5.0005=5.000.

Example:

5.000−2.376\begin{array}{r} 5.000\\ - 2.376\\ \hline \end{array}

Start at the thousandths place. Since 00 is less than 66, regroup. There are zeros in the tenths and hundredths places, so regroup across them:

  • Take 11 one from 55 ones, leaving 44 ones.
  • The 11 one becomes 1010 tenths. Give 11 tenth to the hundredths place, leaving 99 tenths.
  • The 11 tenth becomes 1010 hundredths. Give 11 hundredth to the thousandths place, leaving 99 hundredths.
  • Now there are 1010 thousandths.

The numbers look like this:

4.999−2.376\begin{array}{r} 4.999\\ - 2.376\\ \hline \end{array}

Subtract from right to left:

  • Thousandths: 10−6=410-6=4
  • Hundredths: 9−7=29-7=2
  • Tenths: 9−3=69-3=6
  • Ones: 4−2=24-2=2

So,

5.000−2.376=2.6245.000-2.376=\boxed{2.624}

You can check by adding the difference to the number subtracted:

2.624+2.376=5.0002.624+2.376=5.000

Because the addition returns to the starting number, the subtraction is correct.

Learn by doing: Subtract decimals

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    Subtraction - Decimal Thousandths

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