Number Systems, Decimals And Rational Powers

Question 1

(chalkboard) R

Answer 1

Real numbers

Question 2

real numbers

Answer 2

all numbers on a number line.

Question 3

(chalkboard) Z

Answer 3

The integers

Question 4

The integers

Answer 4

the subset of the real numbers given by

{…,−2,−1,0,1,2,…}.

Question 5

N

Answer 5

natural numbers

Question 6

natural numbers

Answer 6

the subset of the integers given by {1, 2, 3 . . .}.

Question 7

(chalkboard) Q

Answer 7

rational numbers

Question 8

rational numbers

Answer 8

the subset of the real numbers givenby{qp |p,q∈Z}

Question 9

(chalkboard) I

Answer 9

irrational numbers

Question 10

irrational numbers

Answer 10

the real numbers that are not rational

Question 11

root2

Answer 11

The number root2 is irrational

Question 12

Between any two rationals…

Answer 12

there is another rational

Question 13

Let a be a rational number, and b an irrational.

Then a + b is…

Answer 13

irrational

Question 14

Let a be a rational number, and b an irrational.

If a does not equal 0, then ab is…

Answer 14

Irrational

Question 15

Form of a decimal expression

Answer 15

x = a0.a1a2a3 …

Question 16

Which numbers have a decimal expression?

Answer 16

Every real number

Question 17

What is the condition for a periodic decimal expansion?

Answer 17

A real number has periodic decimal expansion if and only if it is rational.

Question 18

The form of a periodic decimal expansion? is called periodic if it has the form
a0.a1 …anb1 …bkb1 …bkb1 … (1)
for a0 ∈ Z and a1,…,an,b1,…,bk ∈ {0,1,…,9}. We abbreviate the expression in (1) by
a0.a1 …anb1 …bk.

Answer 18

Slide 19 decimals

Question 19

The rest of the decimals slides

Answer 19

PowerPoint presentation

Question 20

y^n = x proposition

Answer 20

Let n be a positive integer. If x is a positive real number, then there is a unique positive number y such that y^n = x.

Question 21

The rest of nth roots etc

Answer 21

PowerPoint presentation