Skill: 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 $(5.2-3.78)$.

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

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

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

Now subtract from right to left:

1. In the hundredths column, $(0-8)$ is not possible. Regroup $1$ tenth as $(10)$ hundredths. This leaves $1$ tenth and gives $(10)$ hundredths:

$$10-8=2$$

2. In the tenths column, $(1-7)$ is not possible. Regroup $1$ whole as $(10)$ tenths. This leaves $4$ ones:

$$11-7=4$$

3. In the ones column:

$$4-3=1$$

The decimal point stays in the same column:

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

Therefore,

$$\boxed{5.2-3.78=1.42}$$

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