To determine which of the given numbers is the largest, we compare the values step-by-step. Here are the numbers provided:
- [tex]\(0.7\)[/tex]
- [tex]\(\frac{4}{9}\)[/tex]
- [tex]\(\frac{7}{13}\)[/tex]
- [tex]\(0.549\)[/tex]
- [tex]\(0.67\)[/tex]
First, we compare the decimal numbers directly:
- [tex]\(0.7\)[/tex]
- [tex]\(0.549\)[/tex]
- [tex]\(0.67\)[/tex]
Among these, [tex]\(0.7\)[/tex] is clearly larger than [tex]\(0.549\)[/tex] and [tex]\(0.67\)[/tex].
Next, we need to compare [tex]\(0.7\)[/tex] with the fractions [tex]\(\frac{4}{9}\)[/tex] and [tex]\(\frac{7}{13}\)[/tex].
For [tex]\(\frac{4}{9}\)[/tex]:
Calculating [tex]\(\frac{4}{9}\)[/tex], we get approximately:
[tex]\[ \frac{4}{9} \approx 0.4444 \][/tex]
So, [tex]\(0.7\)[/tex] is larger than [tex]\(\frac{4}{9}\)[/tex] because [tex]\(0.7 > 0.4444\)[/tex].
For [tex]\(\frac{7}{13}\)[/tex]:
Calculating [tex]\(\frac{7}{13}\)[/tex], we get approximately:
[tex]\[ \frac{7}{13} \approx 0.5385 \][/tex]
So, [tex]\(0.7\)[/tex] is larger than [tex]\(\frac{7}{13}\)[/tex] because [tex]\(0.7 > 0.5385\)[/tex].
We have compared [tex]\(0.7\)[/tex] with all other values. Since [tex]\(0.7\)[/tex] is greater than [tex]\(0.549\)[/tex], [tex]\(0.67\)[/tex], [tex]\(\frac{4}{9}\)[/tex], and [tex]\(\frac{7}{13}\)[/tex], it is the largest among the given values.
Therefore, the largest value is:
[tex]\[ 0.7 \][/tex]
