Skill: Order decimals

To order decimals, compare their digits by place value:

1. Line up the decimal points.
2. Add trailing zeros so every number has the same number of decimal places.
3. Compare digits from left to right: tenths, then hundredths, then thousandths.
4. The first different digit tells which number is greater.

Example: Order these decimals from least to greatest:

$$0.7,\quad 0.605,\quad 0.65,\quad 0.56$$

First, write each decimal through the thousandths place by adding zeros when needed:

$$\begin{array}{r} 0.700\\ 0.605\\ 0.650\\ 0.560 \end{array}$$

Now compare the tenths digits:

• $0.560$ has $5$ tenths.
• $0.605$ has $6$ tenths.
• $0.650$ has $6$ tenths.
• $0.700$ has $7$ tenths.

So $0.560$ is least and $0.700$ is greatest. To compare $0.605$ and $0.650$, look at the hundredths digits:

• $0.605$ has $0$ hundredths.
• $0.650$ has $5$ hundredths.

Therefore,

$$\boxed{0.56<0.605<0.65<0.7}$$

Notice that $0.605$ has more digits than $0.65$, but it is not greater. Since $0.65=0.650$, comparing $0.605$ and $0.650$ shows that $0.605$ is smaller.