Skill: Compare decimals to thousandths

To compare decimals, line up the digits by place value:

$$\text{ones} \quad \text{tenths} \quad \text{hundredths} \quad \text{thousandths}$$

You may add zeros at the end of a decimal without changing its value. For example, $(0.7=0.70=0.700)$.

Example: Compare $(3.507)$ and $(3.57)$.

1. Line up the decimal points.
2. Add a zero to $(3.57)$ so both numbers have digits through the thousandths place:

$$\begin{array}{r} 3.507\\ 3.570 \end{array}$$

3. Compare the digits from left to right:
   • Ones: $(3=3)$
   • Tenths: $(5=5)$
   • Hundredths: $(0<7)$

The first place where the digits differ is the hundredths place. Therefore,

$$\boxed{3.507<3.57}$$

Always compare place values from left to right. The first different digit determines which decimal is greater.