QUESTION I 1.1 Given $$ \frac{-7}{3} ; \sqrt[7]{9} ; 2, \dot{3} ; 0 ; \sqrt{4} ; 10 ; 2 \pi $$; which of those numbers are: 1.1.1 Rational numbers (2) 1.1.2 Integers (2) 1.1.3 Whole numbers (2) 1.1.4 Natural numbers (2) 1.1.5 Irrational numbers (2) 1.2 Determine between which whole numbers is $$ \sqrt{24} $$ [13]

Question

UpStudy AI · Accepted Answer

**1.1.1 Rational Numbers**

A number is rational if it can be expressed as a fraction of two integers. Among the given numbers:
- $$\frac{-7}{3}$$ is a fraction of integers.
- $$2,\dot{3}$$ represents a repeating decimal, which can be expressed as a fraction.
- $$0$$ can be written as $$\frac{0}{1}$$.
- $$\sqrt{4}=2$$ is an integer (hence rational).
- $$10$$ is an integer (hence rational).

So, the rational numbers are:  
$$
\frac{-7}{3},\quad 2,\dot{3},\quad 0,\quad \sqrt{4},\quad 10.
$$

**1.1.2 Integers**

Integers are whole numbers and their negatives. From the list:
- $$\sqrt{4}=2$$
- $$0$$
- $$10$$

Thus, the integers are:  
$$
0,\quad 2,\quad 10.
$$

**1.1.3 Whole Numbers**

Whole numbers are the non-negative integers. This means:
- $$0$$
- $$\sqrt{4}=2$$
- $$10$$

Therefore, the whole numbers are:  
$$
0,\quad 2,\quad 10.
$$

**1.1.4 Natural Numbers**

Natural numbers are the positive integers (typically starting at $$1$$). So from our list:
- $$\sqrt{4}=2$$
- $$10$$

Thus, the natural numbers are:  
$$
2,\quad 10.
$$

**1.1.5 Irrational Numbers**

Irrational numbers cannot be written as a fraction of two integers. Among the given numbers:
- $$\sqrt[7]{9}$$ is irrational (since $$9$$ is not a perfect 7th power).
- $$2\pi$$ is irrational (because $$\pi$$ is irrational).

So, the irrational numbers are:  
$$
\sqrt[7]{9},\quad 2\pi.
$$

**1.2 Determining Between Which Whole Numbers $$ \sqrt{24} $$ Lies**

First, note that:
$$
\sqrt{24} = 2\sqrt{6}.
$$

We know:
$$
4^2 = 16 \quad \text{and} \quad 5^2 = 25.
$$

Since:
$$
16 < 24 < 25,
$$
it follows that:
$$
4 < \sqrt{24} < 5.
$$

Thus, $$\sqrt{24}$$ lies between the whole numbers $$4$$ and $$5$$.
**1.1.1 Rational Numbers:** $$\frac{-7}{3},\ 2,\dot{3},\ 0,\ \sqrt{4},\ 10$$ **1.1.2 Integers:** $$0,\ 2,\ 10$$ **1.1.3 Whole Numbers:** $$0,\ 2,\ 10$$ **1.1.4 Natural Numbers:** $$2,\ 10$$ **1.1.5 Irrational Numbers:** $$\sqrt[7]{9},\ 2\pi$$ **1.2** $$\sqrt{24}$$ lies between $$4$$ and $$5$$.

QUESTION I
1.1 Given ; which of those numbers are:
1.1.1 Rational numbers
(2)
1.1.2 Integers
(2)
1.1.3 Whole numbers
(2)
1.1.4 Natural numbers
(2)
1.1.5 Irrational numbers
(2)
1.2 Determine between which whole numbers is
[13]

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Arithmetic Questions

QUESTION I 1.1 Given ; which of those numbers are: 1.1.1 Rational numbers (2) 1.1.2 Integers (2) 1.1.3 Whole numbers (2) 1.1.4 Natural numbers (2) 1.1.5 Irrational numbers (2) 1.2 Determine between which whole numbers is [13]