Question

{-2, -2/7, 0, 0.3, √7, 7.1, √64}

Answer 1

Answers:

• a) √64
• b)  0, √64
• c)  -2, 0,  √64
• d)  -2, -2/7, 0, 0.3, 7.1, √64
• e)  √7
• f)  -2, -2/7, 0, 0.3, √7, 7.1, √64

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Explanations:

Part (a)

The set of natural numbers is {1,2,3,4,...} which is the set of positive whole numbers. We don't include 0. Note that $\sqrt{64} = 8$ to show that it's part of the set of natural numbers. Something like -2 is not in the set, same for -2/7, etc.

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Part (b)

The set of whole numbers is {0,1,2,3,...} which is almost identical to the previous set, but we're now including 0.

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Part (c)

The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...}

We are including the negative values as well as the positive values too. Zero is included.

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Part (d)

Any rational number is of the form p/q, where p,q are integers and q is nonzero. Something like -2/7 is rational. Here we have p = -2 and q = 7.

Any whole number is rational. Eg: 8 = 8/1

Any decimal that terminates is rational. The value 7.1 is the same as 71/10

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Part (e)

If a number isn't rational, then it's considered irrational.

Something like $\sqrt{7}$ is irrational because 7 isn't a perfect square.

The decimal version of the number $\sqrt{7} \approx 2.6457513110646$ goes on forever without any pattern. So this is more evidence it's irrational.

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Part (f)

If your teacher hasn't covered imaginary or complex numbers, then every value you encounter so far is a real number.