Which of the following correctly describes the product below? 0. 159 ‾ × 0. 6 ‾ 0.\overline{159}\times0.\overline{6} 0 . 1 5 9 × 0 . 6

A combination of both rational and irrational

Neither rational nor irrational

Which of the following shows that the product of two irrational numbers can be rational?

2 π 5 × 2 π \frac{2\pi}{5}\times\frac{2}{\pi} 5 2 π × π 2

2 × π \sqrt{2}\times\sqrt{\pi} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> × π <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 π × 2 \frac{2}{\pi}\times\sqrt{2} π 2 × 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

π × 6 \pi\times\sqrt{6} π × 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Which of the following correctly describes the sum of two rational numbers?

Can be rational or irrational depending on the rationals used.

A combination of rational and irrational

Which of the following correctly describes the sum of a rational number and an irrational number?

Can be either rational or irrational depending on the rationals used.

Which of the following correctly describes the quotient below? 0.4 ÷ 0. 6 ‾ 0.4\div0.\overline{6} 0 . 4 ÷ 0 . 6

Neither rational nor irrational

Which of the following correctly describes the product below? 11 10 × 5 \frac{11}{10}\times\sqrt{5} 1 0 1 1 × 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

A combination of both rational and irrational

Neither rational nor irrational

Matt makes a bulletin board in the shape of an isosceles right triangle with an area of exactly 32 square inches. He wants to buy the exact amount of border trim he will need without having any trim left over, but the trim is only sold in rational lengths. Which of the following statements about this situation is true?

Matt can’t buy the exact amount of border trim because he will need an irrational length of trim

Matt can buy the exact amount of border trim because he will need a rational length of trim

Matt can buy the exact amount of border trim because he will need an irrational length of trim

Matt can’t buy the exact amount of border trim because he will need a rational length of trim

Which of the following correctly describes the difference below? 0.4 − 0. 4 ‾ 0.4-0.\overline{4} 0 . 4 − 0 . 4

Neither rational nor irrational

Which of the following correctly describes the sum below? 0. 6 ‾ + π 0.\overline{6}+\pi 0 . 6 + π

Neither rational nor irrational

Which of the following shows that the quotient of two irrational numbers can be rational?

5 2 ÷ 5 \frac{\sqrt{5}}{2}\div\sqrt{5} 2 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ÷ 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

π ÷ 5 π \pi\div\sqrt{5}\pi π ÷ 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> π

2 ÷ 5 \sqrt{2}\div\sqrt{5} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ÷ 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 π ÷ π 2 \sqrt{2}\pi\div\frac{\pi}{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> π ÷ 2 π

Properties of Rational and Irrational Numbers

Authored by Yolanda Goggins

Mathematics

9th Grade

CCSS covered

Used 7+ times

Properties of Rational and Irrational Numbers

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20 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The numbers shown below belong to which of the following subsets of the real numbers? $\left\{-24,\ -5,\ -1,\ 11,\ 14,\ 24\right\}$

Whole Numbers

Irrational Numbers

Integers

Natural Numbers

Tags

CCSS.6.NS.C.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which statement is correct?

Irrational numbers cannot be expressed as fractions or decimals.

Fractions are not real numbers.

Whole numbers are not integers.

All real numbers must be rational.

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

To which subset of the real numbers does
$\frac{\pi}{4}$
Belong?
$\frac{\pi}{4}\approx0.78539816...$

Integers

Irrational Numbers

Whole Numbers

Natural Numbers

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

To which real number subset(s) do the following real numbers belong?
$\left\{-5,\ -4,\ 2,\ 3,\ 7\right\}$

natural numbers

natural and irrational numbers

Integers and rational numbers

Whole numbers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

To which real number subset do the following real numbers belong?
$\left\{14.44,\ \sqrt{25},\ 4\frac{1}{2}\right\}$

Irrational numbers

Natural numbers

Rational numbers

Integers

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

To which real number subset do the following real numbers belong?
$\left\{0,\ 1,\ 4,\ 8,\ 11,\ 12\right\}$

Integers and irrational numbers

Natural numbers and irrational numbers

Irrational numbers and whole numbers

Integers and rational numbers

Tags

CCSS.HSN.RN.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\left\{-10,\ -\frac{9}{2},\ -\frac{1}{2},\ 3,\ \frac{15}{2},\ \frac{19}{2}\right\}$
The numbers shown above belong to which of the following subsets of the real numbers?

Rational Numbers

Integers

Natural Numbers

Irrational Numbers

Tags

CCSS.HSN.RN.B.3

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\left\{\frac{\pi}{4},\ \frac{\pi}{2},\ \sqrt{12},\ \sqrt{20},\ \sqrt{30}\right\}$
The numbers shown above belong to which of the following subsets of the real numbers?

Natural numbers

Rational numbers

Integers

Irrational numbers

Tags

CCSS.HSN.RN.B.3

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Properties of Rational and Irrational Numbers

The numbers shown below belong to which of the following subsets of the real numbers? {−24, −5, −1, 11, 14, 24}\left\{-24,\ -5,\ -1,\ 11,\ 14,\ 24\right\}{−24, −5, −1, 11, 14, 24}

Which statement is correct?

To which subset of the real numbers does π4\frac{\pi}{4}4π​ Belong? π4≈0.78539816...\frac{\pi}{4}\approx0.78539816...4π​≈0.78539816...

To which real number subset(s) do the following real numbers belong? {−5, −4, 2, 3, 7}\left\{-5,\ -4,\ 2,\ 3,\ 7\right\}{−5, −4, 2, 3, 7}

To which real number subset do the following real numbers belong? {14.44, 25, 412}\left\{14.44,\ \sqrt{25},\ 4\frac{1}{2}\right\}{14.44, 25​, 421​}

To which real number subset do the following real numbers belong? {0, 1, 4, 8, 11, 12}\left\{0,\ 1,\ 4,\ 8,\ 11,\ 12\right\}{0, 1, 4, 8, 11, 12}

{−10, −92, −12, 3, 152, 192}\left\{-10,\ -\frac{9}{2},\ -\frac{1}{2},\ 3,\ \frac{15}{2},\ \frac{19}{2}\right\}{−10, −29​, −21​, 3, 215​, 219​} The numbers shown above belong to which of the following subsets of the real numbers?

Which statement is correct?

Which statement is correct?

{π4, π2, 12, 20, 30}\left\{\frac{\pi}{4},\ \frac{\pi}{2},\ \sqrt{12},\ \sqrt{20},\ \sqrt{30}\right\}{4π​, 2π​, 12​, 20​, 30​} The numbers shown above belong to which of the following subsets of the real numbers?

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The numbers shown below belong to which of the following subsets of the real numbers? $\left\{-24,\ -5,\ -1,\ 11,\ 14,\ 24\right\}$

To which subset of the real numbers does
$\frac{\pi}{4}$
Belong?
$\frac{\pi}{4}\approx0.78539816...$

To which real number subset(s) do the following real numbers belong?
$\left\{-5,\ -4,\ 2,\ 3,\ 7\right\}$

To which real number subset do the following real numbers belong?
$\left\{14.44,\ \sqrt{25},\ 4\frac{1}{2}\right\}$

To which real number subset do the following real numbers belong?
$\left\{0,\ 1,\ 4,\ 8,\ 11,\ 12\right\}$

$\left\{-10,\ -\frac{9}{2},\ -\frac{1}{2},\ 3,\ \frac{15}{2},\ \frac{19}{2}\right\}$
The numbers shown above belong to which of the following subsets of the real numbers?

$\left\{\frac{\pi}{4},\ \frac{\pi}{2},\ \sqrt{12},\ \sqrt{20},\ \sqrt{30}\right\}$
The numbers shown above belong to which of the following subsets of the real numbers?