Lesson test: From counting to the real line

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From counting to the real line

1.[2p]
Which equation is the one that forces the negative numbers into existence?

$x + 7 = 3$ , which no natural number solves

Correct

$3 x = 7$ , which no integer solves

The answer is: $x + 7 = 3$, which no natural number solves

$x^{2} = 2$ , which no rational solves

The answer is: $x + 7 = 3$, which no natural number solves

$x^{2} = - 1$ , which no real solves

The answer is: $x + 7 = 3$, which no natural number solves

2.[3p]
The rationals are dense: between any two of them lies another. Why does that not make them complete?

Density says there are no gaps between named rationals, not that every point on the line is one

Correct

Density is only true for positive rationals

The answer is: Density says there are no gaps between named rationals, not that every point on the line is one

Because the average of two rationals is sometimes irrational

The answer is: Density says there are no gaps between named rationals, not that every point on the line is one

Because density fails once the two rationals are very close together

The answer is: Density says there are no gaps between named rationals, not that every point on the line is one

3.[2p]
Write the repeating decimal $0.454545 dots$ as a fraction in lowest terms.

CorrectNot quite: 5/11

4.[2p]
By how much does $(7 / 5)^{2}$ fall short of $2$ ?

CorrectNot quite: 0.04

5.[2p]
Taking $π = 3.14159265$ , what is the absolute error of the approximation $3.14$ ?

CorrectNot quite: 0.00159

6.[1p]
Every irrational number is transcendental.

True

The answer is: False

False

Correct

7.[3p]
Which of these numbers are irrational?

Select all that apply

$\sqrt{2}$

Correct

$π$

Correct

$0.135135 dots$ repeating forever

The answer is: $\sqrt{2}$, $\pi$

$- 17$

The answer is: $\sqrt{2}$, $\pi$

$22 / 7$

The answer is: $\sqrt{2}$, $\pi$

8.[2p]
Put the number systems in order, each one contained in the next.

The integers
The reals
The rationals
The natural numbers

Show the answer

a, b, c, d

9.[3p]
Match each number to the smallest system in the chain that contains it.

$7$
$- 7$
$3 / 8$
$\sqrt{2}$

real
rational
natural
integer

Show the answer

$7$ : natural $- 7$ : integer $3 / 8$ : rational $\sqrt{2}$ : real

1.[2p] Which equation is the one that forces the negative numbers into existence?

2.[3p] The rationals are dense: between any two of them lies another. Why does that not make them complete?

3.[2p] Write the repeating decimal 0.454545dots as a fraction in lowest terms.

4.[2p] By how much does (7/5)2 fall short of 2?

5.[2p] Taking π=3.14159265, what is the absolute error of the approximation 3.14?

6.[1p] Every irrational number is transcendental.

7.[3p] Which of these numbers are irrational?

8.[2p] Put the number systems in order, each one contained in the next.

9.[3p] Match each number to the smallest system in the chain that contains it.

1.[2p]
Which equation is the one that forces the negative numbers into existence?

2.[3p]
The rationals are dense: between any two of them lies another. Why does that not make them complete?

3.[2p]
Write the repeating decimal $0.454545 dots$ as a fraction in lowest terms.

4.[2p]
By how much does $(7 / 5)^{2}$ fall short of $2$ ?

5.[2p]
Taking $π = 3.14159265$ , what is the absolute error of the approximation $3.14$ ?

6.[1p]
Every irrational number is transcendental.

7.[3p]
Which of these numbers are irrational?

8.[2p]
Put the number systems in order, each one contained in the next.

9.[3p]
Match each number to the smallest system in the chain that contains it.