Subtracting Decimals

Line the places up first, exactly as for addition.

Unbundling still works

One whole can be traded for 10 tenths, and one tenth for 10 hundredths.

An example

5 − 2.35 becomes 5.00 − 2.35. Trade a whole for tenths, then a tenth for hundredths.

Check by adding back

If 5 − 2.35 = 2.65, then 2.65 + 2.35 should come to 5.

Unbundling works the same across the point

In 5.2 - 3.47, the hundredths column is empty on top. Write 5.20, then unbundle: one tenth becomes ten hundredths, leaving 5.1 and 10 hundredths. Nothing about the decimal point changes the procedure — a tenth is ten hundredths just as a ten is ten ones.

Pad before you start

Always write both numbers with the same number of decimal places before subtracting. Trying to subtract 3.47 from 5.2 without padding leaves a column with nothing above it, and the usual reflex — bringing down the 7 — gives a badly wrong answer.

Check by adding back

5.2 - 3.47 = 1.73, and 1.73 + 3.47 = 5.20. The check uses a different operation, so it catches errors that rereading would not. With decimals it also confirms you kept the point in the right place.

Counting up is often easier

From 3.47 to 3.50 is 0.03; to 4.00 is 0.50 more; to 5.20 is 1.20 more. Total 1.73. When the numbers are close or the top number has awkward zeros, counting up avoids unbundling entirely and is less error-prone.