Question

label each point on the number line with the correct value. click each dot on the image to select an answer. choices: \\(\frac{7}{9}\\) \\(\frac{10}{9}\\) 0.62 \\(\leftarrow\\) \\(\frac{1}{3}\\) \\(\circ^a\\) \\(\frac{2}{3}\\) \\(\circ^b\\) 1 \\(\circ^c\\) \\(1\frac{1}{3}\\) \\(\
ightarrow\\)

Explanation:

Step1: Convert to decimals

Convert each number to decimal for easier comparison.

• $\frac{7}{9} \approx 0.777\ldots$
• $\frac{10}{9} \approx 1.111\ldots$
• $0.62 = 0.62$
• $\frac{1}{3} \approx 0.333\ldots$
• $\frac{2}{3} \approx 0.666\ldots$
• $1 = 1$
• $1\frac{1}{3} \approx 1.333\ldots$

Step2: Match to positions

• Point \(a\) is near \(\frac{2}{3} \approx 0.666\), but \(0.62\) is \(0.62\) (closer to \(\frac{2}{3}\)? Wait, \(0.62 < 0.666\), so \(a\) should be \(0.62\)? Wait no, let's re - check. Wait \(\frac{1}{3}\approx0.333\), \(\frac{2}{3}\approx0.666\), \(1\), \(1\frac{1}{3}\approx1.333\).
• \(0.62\) is less than \(\frac{2}{3}\approx0.666\), so \(a\): \(0.62\) (since \(0.62\) is between \(\frac{1}{3}\) and \(\frac{2}{3}\), closer to \(\frac{2}{3}\) but less than \(\frac{2}{3}\)).
• \(b\): \(\frac{7}{9}\approx0.777\), which is greater than \(\frac{2}{3}\approx0.666\) and less than \(1\), so \(b = \frac{7}{9}\).
• \(c\): \(\frac{10}{9}\approx1.111\), which is between \(1\) and \(1\frac{1}{3}\approx1.333\), so \(c=\frac{10}{9}\).

Answer:

• \(a\): \(0.62\)
• \(b\): \(\frac{7}{9}\)
• \(c\): \(\frac{10}{9}\)