Question

Danny, a grade 10 math student, completed the following chart. Review Danny's work. If there

Answer 1

Answer:

$\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3\dfrac{3}{9}&&&& \checkmark&&\checkmark\\\sqrt{11} &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}$

Step-by-step explanation:

The given numbers and their categories are;

1) $-3\dfrac{3}{9}$  is not a natural number, because, natural numbers are whole number positive integers. It is not an integer, because it is a fraction.

It is a real number, because it has no imaginary part and it is a rational number because it can be expressed as a fraction

2) √11 is not a rational number, because it cannot be expressed as a fraction, and it is real number because it has no imaginary parts.

Therefore, is an irrational and real number

3) 125; The options selected are correct

4) 4·∛125 = 4 × 5 = 20; The options selected are correct

5) 7.$\overline {17}$ = 710/99; Therefore, 7.$\overline {17}$ is a rational number and it is also a real number as all natural, whole, integers, rational, and irrational numbers are real numbers

We get;

$\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3\dfrac{3}{9}&&&& \checkmark&&\checkmark\\\sqrt{11} &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}$