Number Theory and Real Number Systems

Question 1

The set consisting of the natural numbers, 0, and the negatives of the natural numbers is called the set of ________.

Answer 1

integers

Question 2

What is another name for natural numbers?

Answer 2

positive integers

Question 3

What are the two ways that positive integers can be written?

Answer 3

1. Use a “+” sign. For example, +4 is “positive four”.
2. Do not write any sign. For example, 4 is also “positive four”.

Question 4

The ________ _______ is a graph we use to visualize the set of integers, as well as sets of other numbers.

Answer 4

number line

Question 5

The _______ ______ of an integer a, denoted by |a|, is the distance from 0 to a on the number line

Answer 5

absolute value

Question 6

Because absolute value describes a distance, it is never _________.

Answer 6

negative

Question 7

The set of _______ ______ is the set of all numbers which can be expressed in the form a/b, where a and b are integers and b is not equal to 0

Answer 7

rational numbers

Question 8

A mixed number consists of the ____ of an _______ and a ________ _________, expressed without the use of an addition sign.

Answer 8

• sum
• integer
• rational number

Question 9

An ______ _______ is a rational number whose numerator is greater than its denominator

Answer 9

improper fraction

Question 10

terminating decimal vs repeating decimal

Answer 10

• terminating decimal is when the decimal stops
• repeating decimal is when the decimal keeps repeating indefinitely

Question 11

The set of _________ ___________ is the set of numbers whose decimal
representations are neither terminating nor repeating.

Answer 11

irrational numbers

Question 12

A _______ ______ is a number that is the square of a whole number

Answer 12

perfect square

Question 13

The principal square root of a nonnegative number n, written √n , is the:

Answer 13

positive number that when multiplied by itself gives n