Skill: Compare and order positive rational numbers

Positive rational numbers can be written as fractions, decimals, or percents. To compare them, rewrite them in the same form, then use place value.

Example: Order $\frac{3}{5}$, $0.72$, $65\%$, and $\frac{1}{2}$ from least to greatest.

1. Rewrite each number as a decimal:

$$\frac{3}{5}=0.6$$ $$65\%=0.65$$ $$\frac{1}{2}=0.5$$

2. Now compare the decimals:

$$0.5,\quad 0.6,\quad 0.65,\quad 0.72$$

The tenths digits show that $0.5<0.6<0.7$. Between $0.6$ and $0.72$, compare the hundredths: $0.65<0.72$.

3. Replace each decimal with its original form:

$$\boxed{\frac{1}{2}<\frac{3}{5}<65\%<0.72}$$

All four numbers represent positive quantities, so they can be compared on a number line. The number farther to the right is greater. Always compare equivalent forms and use place value; do not compare numerators or denominators by themselves.