Learning Materials

Structured explanations, one concept at a time.

Ordering and Comparing Whole Numbers, Decimals, Fractions and Percentages

To order numbers means to arrange them from smallest to largest (or vice versa). To compare numbers means to decide which is greater or smaller. When numbers are written in different forms, the safest approach is to convert them into the same form before comparing.

 

A reliable method is to convert everything into decimals, because decimals are easy to place on a number line.
Whole numbers can be written as decimals by adding a decimal point and zeros. Fractions are converted by dividing the numerator by the denominator. Percentages are converted by dividing by \(100\).

$$
\frac{3}{4} = 0.75
$$

$$
65% = 0.65
$$

 

Once all values are in decimal form, you can compare them directly using place value.

$$
0.8 > 0.75 > 0.65 > 0.6
$$

 

When ordering fractions only, you can also use a common denominator. Convert each fraction so they all have the same denominator, then compare the numerators.

$$
\frac{2}{5} = \frac{8}{20}, \quad \frac{3}{4} = \frac{15}{20}
$$

Since \(15 > 8\), \(\frac{3}{4}\) is larger than \(\frac{2}{5}\).

 

Percentages can often be compared quickly by remembering that \(100%\) represents one whole. Any percentage greater than \(100%\) is greater than \(1\), and any percentage less than \(100%\) is less than \(1\).

 

Always check that all numbers are being compared in the same form, and take care with decimals that have different numbers of decimal places.