Question

use the number line below for exercises 1-8.
match each number with its graph.

1. (|-8|)
2. (-|-4|)
3. (-1.overline{6})
4. (-8)

write true or false. the letters name numbers on the number line shown above.

1. (f < a)
2. (b > g)
3. (a > k)
4. (h > c)

integers and the real world

1. state the integers that correspond to the situation.

the qattara depression in egypt is 436 ft below sea level. mount catherine in egypt is 8625 ft above sea level.
the rational numbers
graph the number on the number line.

1. (3.14)
2. (-\frac{11}{3})

Explanation:

Step1: Evaluate absolute value

$|-8| = 8$

Step2: Match to number line point

Point $g$ is at 8.

Step3: Evaluate negative absolute value

$-|-4| = -4$

Step4: Match to number line point

Point $K$ is at -4.

Step5: Convert repeating decimal

$-1.\overline{6} = -\frac{5}{3} \approx -1.67$

Step6: Match to number line point

Point $H$ is at $-1.\overline{6}$.

Step7: Locate -8 on number line

Point $A$ is at -8.

Step8: Compare F and A values

$F=8$, $A=-8$; $8 < -8$ is False.

Step9: Compare B and G values

$B=4$, $G=3$; $4 > 3$ is True.

Step10: Compare A and K values

$A=-8$, $K=-4$; $-8 > -4$ is False.

Step11: Compare H and C values

$H=-1.\overline{6}$, $C=-1$; $-1.\overline{6} > -1$ is False.

Step12: Assign integers to elevation

Below sea level = negative, above = positive.

Step13: Graph 3.14 on number line

3.14 lies between 3 and 4, closer to 3.

Step14: Convert fraction to decimal

$-\frac{11}{3} \approx -3.67$

Step15: Graph $-\frac{11}{3}$ on number line

$-3.67$ lies between -4 and -3, closer to -4.

Answer:

1. $|-8|$ matches point $g$
2. $-|-4|$ matches point $K$
3. $-1.\overline{6}$ matches point $H$
4. $-8$ matches point $A$
5. False
6. True
7. False
8. False
9. Qattara Depression: $-436$; Mount Catherine: $8625$
10. (Graph: Place a point between 3 and 4, 0.14 units to the right of 3 on the provided number line)
11. (Graph: Place a point between -4 and -3, $\frac{1}{3}$ units to the right of -4 on the provided number line)