To order the given values [tex]\(45 \%, 0.7, \frac{5}{2}, 25\%, \frac{1}{8}\)[/tex] by increasing size, let's first convert all of these values to a common form, such as decimals.
1. Converting Percentages to Decimals:
- [tex]\(45 \%\)[/tex] can be written as [tex]\( \frac{45}{100} \)[/tex], which is [tex]\( 0.45 \)[/tex].
- [tex]\(25 \%\)[/tex] can be written as [tex]\( \frac{25}{100} \)[/tex], which is [tex]\( 0.25 \)[/tex].
2. Fraction to Decimal Conversion:
- The fraction [tex]\( \frac{5}{2} \)[/tex] can be simplified to [tex]\( 2.5 \)[/tex].
- The fraction [tex]\( \frac{1}{8} \)[/tex] can be calculated as [tex]\( 0.125 \)[/tex].
Now, we have the values in decimal form:
- [tex]\( 45 \% = 0.45 \)[/tex]
- [tex]\( 0.7 \)[/tex]
- [tex]\( \frac{5}{2} = 2.5 \)[/tex]
- [tex]\( 25 \% = 0.25 \)[/tex]
- [tex]\( \frac{1}{8} = 0.125 \)[/tex]
Next, let's arrange these decimals in increasing order:
- [tex]\( 0.125 \)[/tex]
- [tex]\( 0.25 \)[/tex]
- [tex]\( 0.45 \)[/tex]
- [tex]\( 0.7 \)[/tex]
- [tex]\( 2.5 \)[/tex]
So, ordering the original values by increasing size:
[tex]\[
\frac{1}{8}, 25 \%, 45 \%, 0.7, \frac{5}{2}
\][/tex]
