1Cademy - Writing $$-19$$ and $$8.41$$ as Ratios of Two Integers

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Rational Number

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Writing $-19$ and $8.41$ as Ratios of Two Integers

Demonstrate that both an integer and a terminating decimal are rational by expressing each as a ratio of two integers.

Part (a) — Write $-19$ as a ratio of two integers. Any integer can be placed over a denominator of $1$ without changing its value:

$-19 = \frac{-19}{1}$

Since $-19$ and $1$ are both integers and the denominator is not zero, $-19$ satisfies the definition of a rational number.

Part (b) — Write $8.41$ as a ratio of two integers. The decimal $8.41$ has two decimal places, so its last digit sits in the hundredths position. Writing it as a fraction with a power-of-ten denominator gives:

$8.41 = \frac{841}{100}$

Because $841$ and $100$ are both integers and $100 \neq 0$ , the number $8.41$ is rational.

These two cases illustrate a general pattern: every integer is rational (use denominator $1$ ), and every terminating decimal is rational (use the appropriate power of ten as the denominator).

Updated 2026-04-21

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OpenStax Elementary Algebra

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