College

Example 3: Compare Rational Numbers

Compare [tex]-0.51[/tex] and [tex]-\frac{12}{25}[/tex].

Step 1: Write the fraction as a decimal.
\[ [tex]-\frac{12}{25} = \square[/tex] \]
Rewrite the fraction as a decimal so that the values are in the same form.

Step 2: Graph the values on the number line.

Answer :

To compare the rational numbers [tex]\(-0.51\)[/tex] and [tex]\(-\frac{12}{25}\)[/tex], follow these steps:

Step 1: Convert the Fraction to a Decimal

First, we need to convert the fraction [tex]\(-\frac{12}{25}\)[/tex] into a decimal. To do this, divide the numerator by the denominator:

[tex]\[
-\frac{12}{25} = -0.48
\][/tex]

Now, we have two decimals: [tex]\(-0.51\)[/tex] and [tex]\(-0.48\)[/tex].

Step 2: Compare the Decimal Values

Next, compare the two decimal values we have: [tex]\(-0.51\)[/tex] and [tex]\(-0.48\)[/tex].

Since [tex]\(-0.51\)[/tex] is a smaller number than [tex]\(-0.48\)[/tex] on the number line (because it is more negative), [tex]\(-0.51\)[/tex] is less than [tex]\(-0.48\)[/tex].

So, when you compare [tex]\(-0.51\)[/tex] and [tex]\(-\frac{12}{25}\)[/tex], you find that:

[tex]\[
-0.51 < -\frac{12}{25}
\][/tex]

Step 3: Graph on the Number Line (Optional)

To visually confirm this comparison, you can plot both values on a number line. You would place [tex]\(-0.51\)[/tex] to the left of [tex]\(-0.48\)[/tex], which aligns with the conclusion that [tex]\(-0.51\)[/tex] is less than [tex]\(-0.48\)[/tex].