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].
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].