Choose the correct description of the number set.(4 points)

Question

(√8 , √9 , √10 )
(-7.4, 0, 3.232323..., √25 )
(-⅚ , ⅞ , π/2 )
(√2 , √5 , 𝛑 )

responses
rational numbers only
irrational numbers only
both rational and irrational numbers

Match the number with the correct description.(5 points)
0.123124125….
√49
0.567
√17
0.898989…

responses
rational non-repeating/non-terminating decimal
irrational non-repeating/non-terminal decimal
irrational square root of a non-perfect square
irrational repeating decimal
rational terminating decimal
rational square root of a non-perfect square
rational square root of a perfect square
irrational square root of a perfect square
irrational terminating decimal
rational repeating decimal

Which of the following expressions and answers would match with the scenario:

Bob owed Jim $7 and also earned $25 mowing the grass for his dad.

(1 point)
Responses

Irrational answer: Bob still owes $ in the end: -7 - 25 = - 32
Irrational answer: Bob still owes $ in the end: -7 - 25 = - 32

Rational/Integer answer: Bob has some $ in his pocket in the end: -7 + 25 = 18
Rational/Integer answer: Bob has some $ in his pocket in the end: -7 + 25 = 18

Whole number answer: Bob breaks even and does not owe $ or have any $ in his pocket.
Whole number answer: Bob breaks even and does not owe $ or have any $ in his pocket.

Rational answer: Bob has some $ in his pocket in the end: 7 - 25 = -18
Rational answer: Bob has some $ in his pocket in the end: 7 - 25 = -18

Irrational/Integer answer: Bob still owes $ in the end; 7 - 25 = - 18
Irrational/Integer answer: Bob still owes $ in the end; 7 - 25 = - 18

Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747.... = what fraction?(5 points)
x = 0.47474747
subtract x = 0.474747
100x = 47.474747
x = 47/99
99x = 47

Order the numbers from largest to smallest:

Largest number at the top

.

.

.

.

.

Smallest number at the bottom

(6 points)
-3
2(3)
V--9
|5|
-3 (2)
|-4|

Between which pair of rational numbers on a number line does 18−−√
lie?(1 point)
Responses

Between 9 and 9.2
Between 9 and 9.2

Between 4.3 and 4.5
Between 4.3 and 4.5

Between 4.2 and 4.3
Between 4.2 and 4.3

Between 8.9 and 9.1

Identify the MOST SPECIFIC set to which each of the following numbers belongs.(7 points)
42−−√
4.56666....
36−−√
6.263
911
0
−25

responses
natural number
integer
whole number
irrational number
rational number

For the inequality x≥−4
, which number(s) listed makes the inequality true? (Check all that apply)(2 points)
Responses

−4611
negative 46 over 11

-5
-5

-10.1010
-10.1010

−10−−√
negative square root of 10

-2.101101110...

Answer 1

Let's tackle each section one by one:

Number Set Description:

1. (√8, √9, √10):

   • √9 is rational (3).
   • √8 and √10 are irrational.
   • Description: both rational and irrational numbers.

2. (-7.4, 0, 3.232323...):

   • -7.4 and 0 are rational. 3.232323... is also rational (as it's a repeating decimal).
   • Description: rational numbers only.

3. (-⅚, ⅞, π/2):

   • -⅚ and ⅞ are rational, while π/2 is irrational.
   • Description: both rational and irrational numbers.

4. (√2, √5, π):

   • All three are irrational numbers.
   • Description: irrational numbers only.

Match Number with Description:

1. 0.123124125…:

   • This is a rational non-repeating/non-terminating decimal.

2. √49:

   • This is a rational square root of a perfect square (7).

3. 0.567:

   • This is a rational terminating decimal.

4. √17:

   • This is an irrational square root of a non-perfect square.

5. 0.898989…:

   • This is a rational repeating decimal.

Expression Matching Scenario:

Bob's situation is:

• Owes $7 (−7) and earns $25 (+25) will be expressed as:
• Rational/Integer answer: Bob has some $ in his pocket in the end: -7 + 25 = 18.

Steps to Change Repeating Decimal to Fraction:

1. x = 0.474747…
2. 100x = 47.474747…
3. subtract x = 0.474747…
4. 99x = 47
5. x = 47/99

Order from Largest to Smallest:

1. |5| = 5
2. |−4| = 4
3. 2(3) = 6
4. V(−9) (not a real number)
5. -3
6. -3(2) = -6

Largest to Smallest:

• 5, 4, 6, V(−9), -3, -6

Between Rational Numbers for √18 (≈4.24):

• Between 4.2 and 4.3.

Most Specific Set for Each Number:

1. √42: irrational number.
2. 4.56666…: rational number.
3. √36: rational number (6).
4. 6.263: rational number.
5. 911: rational number (integer).
6. 0: rational number (integer).
7. −25: rational number (integer).

Inequality x ≥ −4:

The numbers that make the inequality true are:

• −46/11
• −2.101101110…

(Note: Check each of these to see if they fulfill the inequality; the negative square root of 10 is less than −4 and does not satisfy the inequality.)

I hope this helps with your questions! If you have more queries, feel free to ask.