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Chapter 1.1, Problem 1E

BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
ISBN: 9781305071759

Solutions

Chapter
Section
BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
ISBN: 9781305071759

(a)

To determine

To give: An example of a natural number.

Answer

The example of a natural number is 2.

Explanation

Natural numbers are the numbers which are used in counting.

That is, ={1,2,3,4,5,}.

Hence, natural numbers will be greater than zero and will have no fractions.

Therefore, the example of a natural number is 2.

(b)

To determine

To give: An example of an integer that is not a natural number.

Answer

An integer that is not a natural number is −4.

Explanation

Integers are the set of all whole numbers which includes positive, negative values and also includes zero. And it is denoted by a letter .

That is, ={,3,2,1,0,1,2,3,}.

Natural numbers are counting numbers which means that they are greater than zero.

An example of an integer that is not a natural number can be a negative number or zero.

Therefore, an example of an integer that is not a natural number is −4.

(c)

To determine

To give: An example of a rational number that is not an integer.

Answer

The example of a rational number that is not an integer is 45.

Explanation

A rational number is a number which is in the form pq where p and q are integers and q0. Also, if the decimal expansion of any number terminates or repeats, then such a number is called as a rational number.

For example; 23,12,45, are rational numbers.

A rational number that is not an integer can be any fraction because integers are the set of all whole numbers which are positive, negative numbers and also includes zero.

Therefore, an example of a rational number that is not an integer is 45.

(d)

To determine

To give: An example of an example of an irrational number.

Answer

The example of an irrational number is 2.

Explanation

An irrational number is a number which cannot be expressed in the form pq, where p and q are integers and q0. Also, if the decimal expansion of any number does not terminate or repeat, then such a number is called an irrational number.

For example; 2=1.414213,π=3.1413 are irrational numbers.

Therefore, the example of an irrational number is 2.

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