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22. Arrange the following in order: [tex]$\frac{-7}{10}, \frac{8}{-15}, \frac{19}{30}, \frac{-2}{-5}$[/tex]

a) [tex]$\frac{-7}{10}, \frac{8}{-15}, \frac{19}{30}, \frac{-2}{-5}$[/tex]
b) [tex]$\frac{-2}{-5}, \frac{19}{30}, \frac{-7}{10}, \frac{8}{-15}$[/tex]
c) [tex]$\frac{19}{30}, \frac{-2}{-5}, \frac{-7}{10}, \frac{8}{-15}$[/tex]
d) [tex]$\frac{8}{-15}, \frac{19}{30}, \frac{-7}{10}, \frac{-2}{-5}$[/tex]

23. Round off 112.999 to the nearest whole number:

a) 112.100
b) 112.000
c) 113
d) 112.109

24. Identify the point that represents the fraction [tex]$\frac{3}{2}$[/tex] on the number line:

a) D
b) C
c) B
d) A

25. Identify an irrational number:

a) [tex]$\frac{4}{9}$[/tex]
b) [tex]$\sqrt{24}$[/tex]
c) [tex]$\sqrt{169}$[/tex]
d) 2.5

26. If the division is exact, i.e., zero remainder is reached, then it is called a ----- decimal.

a) terminating
b) recurring
c) persistent
d) frequent

Sagot :

GinnyAnsweridn
Let's solve the problems step-by-step:

### Problem 22: Arrange the Fractions in Order

First, let's evaluate the fractions:
- [tex]\(\frac{-7}{10} = -0.7\)[/tex]
- [tex]\(\frac{8}{-15} = -\frac{8}{15} \approx -0.533\)[/tex]
- [tex]\(\frac{19}{30} \approx 0.633\)[/tex]
- [tex]\(\frac{-2}{-5} = \frac{2}{5} = 0.4\)[/tex]

Now, we arrange them in ascending order:
- [tex]\(\frac{8}{-15}\)[/tex] (\approx -0.533)
- [tex]\(\frac{-7}{10}\)[/tex] (-0.7)
- [tex]\(\frac{2}{5}\)[/tex] (0.4)
- [tex]\(\frac{19}{30}\)[/tex] (0.633)

Thus, the correct order is:
a) [tex]\(\frac{8}{-15}, \frac{-7}{10}, \frac{2}{5}, \frac{19}{30}\)[/tex]

### Problem 23: Round off 112.999 to the Nearest Whole Number

When rounding 112.999 to the nearest whole number, you look at the decimal part (0.999), which is greater than 0.5, so you round up.

Therefore, the rounded number is:
c) 113

### Problem 24: Identify the Point that Represents [tex]\(\frac{3}{2}\)[/tex] on the Number Line

The fraction [tex]\(\frac{3}{2}\)[/tex] equals 1.5.

Given the points:
- [tex]\(D = \frac{4}{3} \approx 1.333\)[/tex]
- [tex]\(C = \frac{3}{2} = 1.5\)[/tex]
- [tex]\(B = \frac{5}{3} \approx 1.667\)[/tex]
- [tex]\(A = 2\)[/tex]

The fraction [tex]\(\frac{3}{2}\)[/tex] corresponds to:
b) [tex]\(C\)[/tex]

### Problem 25: Identify an Irrational Number

An irrational number cannot be expressed as a simple fraction and has a non-terminating, non-repeating decimal expansion.

- [tex]\(\frac{4}{9}\)[/tex] is a rational number.
- [tex]\(\sqrt{24} \approx 4.899\)[/tex], which is irrational.
- [tex]\(\sqrt{169} = 13\)[/tex], which is rational.
- 2.5 is a rational number.

The irrational number is:
b) [tex]\(\sqrt{24}\)[/tex]

### Problem 26: If the Division is Exact (Zero Remainder Reached) then It is Called which Decimal?

When the division result has no remainder, it’s a terminating decimal.

So the answer is:
a) terminating

Putting it all together, the answers to the problems are:
1. a) [tex]\(\frac{-7}{10}, \frac{8}{-15}, \frac{19}{30}, \frac{-2}{-5}\)[/tex]
2. c) 113
3. b) [tex]\(C\)[/tex]
4. b) [tex]\(\sqrt{24}\)[/tex]
5. a) terminating
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