Question

13
plot, order, and compare the following on horizontal and vertical number lines
nso.1.1
positive integers, fractions, decimals, and percents when given in different
forms (l4)
write the set of values in
order from least to greatest
using inequality symbols:
\\(\frac{3}{4}\\) , 0.68 , 7 , \\(1\frac{1}{2}\\)
\\(\underline{\quad\quad} < \underline{\quad\quad} < \underline{\quad\quad} < \underline{\quad\quad}\\)
write the set of values in
order from least to greatest
using inequality symbols:
2.05 , \\(1\frac{1}{4}\\) , 2.68 , \\(2\frac{1}{2}\\)

Explanation:

Step1: Convert fractions to decimals

Convert \(\frac{3}{4}\) to decimal: \(\frac{3}{4} = 0.75\)
Convert \(1\frac{1}{2}\) to decimal: \(1\frac{1}{2}=1.5\)

Step2: Compare the decimals

Now we have the values as decimals: \(0.68\), \(0.75\) (from \(\frac{3}{4}\)), \(1.5\) (from \(1\frac{1}{2}\)), and \(7\).
Comparing these decimals: \(0.68 < 0.75 < 1.5 < 7\).

Step3: Substitute back the original forms

Substitute \(0.75\) with \(\frac{3}{4}\), \(1.5\) with \(1\frac{1}{2}\). So the order is \(0.68 < \frac{3}{4} < 1\frac{1}{2} < 7\).

For the second set:

Step1: Convert mixed numbers to decimals

Convert \(1\frac{1}{4}\) to decimal: \(1\frac{1}{4}=1.25\)
Convert \(2\frac{1}{2}\) to decimal: \(2\frac{1}{2}=2.5\)

Step2: Compare the decimals

Now we have the values as decimals: \(1.25\) (from \(1\frac{1}{4}\)), \(2.05\), \(2.5\) (from \(2\frac{1}{2}\)), and \(2.68\).
Comparing these decimals: \(1.25 < 2.05 < 2.5 < 2.68\).

Step3: Substitute back the original forms

Substitute \(1.25\) with \(1\frac{1}{4}\), \(2.5\) with \(2\frac{1}{2}\). So the order is \(1\frac{1}{4} < 2.05 < 2\frac{1}{2} < 2.68\).

Answer:

First set: \(0.68 < \frac{3}{4} < 1\frac{1}{2} < 7\)
Second set: \(1\frac{1}{4} < 2.05 < 2\frac{1}{2} < 2.68\)