To arrange the given rational numbers [tex]\(\frac{3}{4}, -2 \frac{1}{2}, 0, -1 \frac{1}{7}, \)[/tex] and [tex]\(2\)[/tex] in ascending order, follow these steps:
1. Convert all mixed numbers to improper fractions or decimals for easier comparison.
- [tex]\( \frac{3}{4} \)[/tex] is already a fraction.
- [tex]\( -2 \frac{1}{2} \)[/tex] can be converted to [tex]\( -2.5 \)[/tex].
- [tex]\( 0 \)[/tex] is already a number.
- [tex]\( -1 \frac{1}{7} \)[/tex] can be converted to [tex]\( -1 - \frac{1}{7} = -1.1428571428571428 \approx -1.14 \)[/tex].
- [tex]\( 2 \)[/tex] is already a number.
2. List the decimals:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\( -2 \frac{1}{2} = -2.5 \)[/tex]
- [tex]\( 0 = 0 \)[/tex]
- [tex]\( -1 \frac{1}{7} \approx -1.1428571428571428 \)[/tex]
- [tex]\( 2 = 2 \)[/tex]
3. Arrange these in ascending order:
- Start with the smallest number. In this case, it's [tex]\( -2.5 \)[/tex].
- Next is [tex]\( -1.1428571428571428 \)[/tex].
- Then [tex]\( 0 \)[/tex].
- Followed by [tex]\( 0.75 \)[/tex].
- Finally, [tex]\( 2 \)[/tex].
So, the given rational numbers in ascending order are:
[tex]\[ -2.5, -1.1428571428571428, 0, 0.75, 2 \][/tex]
