Question

drag the appropriate symbol to the white rectangle in order to make the statement true. 4.02 4.2 0.21 2.1 -\frac{16}{3} -5\frac{1}{3} \frac{7}{16} \frac{14}{32} -0.25 -0.3 9.\overline{9} 9.975 3\frac{5}{8} \frac{30}{8} 10\frac{2}{3} \frac{61}{6} \frac{1}{9} \frac{1}{8} 0.8 0.08 drag these ordering rational numbers

Explanation:

Step1: Compare 4.02 and 4.2

4.02 has a 0 in the tenths - place and 4.2 has a 2 in the tenths - place. So 4.02 < 4.2.

Step2: Compare 0.21 and 2.1

0.21 has 0 in the units - place and 2.1 has 2 in the units - place. So 0.21 < 2.1.

Step3: Convert - 5\frac{1}{3} to an improper fraction

- 5\frac{1}{3}=-\frac{16}{3}. So -\frac{16}{3}=-5\frac{1}{3}.

Step4: Simplify \frac{14}{32}

\frac{14\div2}{32\div2}=\frac{7}{16}. So \frac{7}{16}=\frac{14}{32}.

Step5: Compare - 0.25 and - 0.3

The absolute value of - 0.25 is 0.25 and the absolute value of - 0.3 is 0.3. Since 0.25 < 0.3, then - 0.25 > - 0.3.

Step6: Compare 9.\overline{9} and 9.975

9.\overline{9}=9.999\cdots>9.975.

Step7: Convert 3\frac{5}{8} to an improper fraction

3\frac{5}{8}=\frac{29}{8}<\frac{30}{8}.

Step8: Convert 10\frac{2}{3} to an improper fraction

10\frac{2}{3}=\frac{32}{3}=\frac{64}{6}>\frac{61}{6}.

Step9: Compare \frac{1}{9} and \frac{1}{8}

When the numerators are the same, the fraction with the larger denominator is smaller. 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Answer:

Step1: Compare 4.02 and 4.2

4.02 has a 0 in the tenths - place and 4.2 has a 2 in the tenths - place. So 4.02 < 4.2.

Step2: Compare 0.21 and 2.1

0.21 has 0 in the units - place and 2.1 has 2 in the units - place. So 0.21 < 2.1.

Step3: Convert - 5\frac{1}{3} to an improper fraction

• 5\frac{1}{3}=-\frac{16}{3}. So -\frac{16}{3}=-5\frac{1}{3}.

Step4: Simplify \frac{14}{32}

\frac{14\div2}{32\div2}=\frac{7}{16}. So \frac{7}{16}=\frac{14}{32}.

Step5: Compare - 0.25 and - 0.3

The absolute value of - 0.25 is 0.25 and the absolute value of - 0.3 is 0.3. Since 0.25 < 0.3, then - 0.25 > - 0.3.

Step6: Compare 9.\overline{9} and 9.975

9.\overline{9}=9.999\cdots>9.975.

Step7: Convert 3\frac{5}{8} to an improper fraction

3\frac{5}{8}=\frac{29}{8}<\frac{30}{8}.

Step8: Convert 10\frac{2}{3} to an improper fraction

10\frac{2}{3}=\frac{32}{3}=\frac{64}{6}>\frac{61}{6}.

Step9: Compare \frac{1}{9} and \frac{1}{8}

When the numerators are the same, the fraction with the larger denominator is smaller. 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