1Cademy - Comparing Fractions and Integers as Ratios and Decimals

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Rational Number

Example

Comparing Fractions and Integers as Ratios and Decimals

The following table illustrates that both fractions and integers qualify as rational numbers by presenting each in three forms — the original number, its ratio-of-integers form, and its decimal form.

	$\frac{4}{5}$	$-\frac{7}{8}$	$\frac{13}{4}$	$-\frac{20}{3}$	$-2$	$-1$	$0$	$1$	$2$	$3$
Ratio of Integers	$\frac{4}{5}$	$-\frac{7}{8}$	$\frac{13}{4}$	$-\frac{20}{3}$	$\frac{-2}{1}$	$\frac{-1}{1}$	$\frac{0}{1}$	$\frac{1}{1}$	$\frac{2}{1}$	$\frac{3}{1}$
Decimal Form	$0.8$	$-0.875$	$3.25$	$-6.\overline{6}$	$-2.0$	$-1.0$	$0.0$	$1.0$	$2.0$	$3.0$

Key observations:

Fractions such as $\frac{4}{5}$ and $-\frac{7}{8}$ are already written as ratios of two integers, so they are rational by definition.
Integers become ratios by placing them over a denominator of $1$ (e.g., $-2 = \frac{-2}{1}$ ).
Some decimal equivalents terminate (e.g., $\frac{4}{5} = 0.8$ and $\frac{13}{4} = 3.25$ ), while $-\frac{20}{3}$ produces a repeating decimal ( $-6.\overline{6}$ ). Both outcomes confirm the numbers are rational.

Updated 2026-04-21

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OpenStax Elementary Algebra

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