Kinds of real numbers: rational and irrational

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Kira deals six cards from a number deck: √196, √77, π, 0.8, 0.3636…, √88. How many of the cards show an irrational number?

   3
2. 2.

   Luz deals seven cards from a number deck: √225, √56, √91, √95, √78, 0.9, 0.7272…. How many of the cards show an irrational number?

   4
3. 3.

   Pia picks cards −18, √41 and 0. What is the smallest group that holds all of these numbers?

   • integers
   • real numbers
   • irrational numbers
   • rational numbers
4. 4.

   Ren picks cards √17, 9, π and 0.5. What is the smallest group that holds all of these numbers?

   • rational numbers
   • irrational numbers
   • real numbers
   • integers
5. 5.

   Ari gets two clues about a mystery number: it is a real number, and it is not rational. Which number fits both clues?

   • 6.4
   • 0.1818…
   • √64
   • √48

6. Read this first

   Use this

   Number line from -4 to 4, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. The real numbers are every mark on the line.

7. 6.

   Bo reads four claims about number groups on a sticky note. Which claim is true?

   • Every real number is an integer.
   • Every integer is a real number.
   • Irrational numbers have no place on the number line.
   • Every square root is an irrational number.
8. 7.

   Jun reads four claims about number groups on a sticky note. Which claim is true?

   • Rational and irrational numbers together make up all the real numbers.
   • Rational numbers make up all the real numbers.
   • Whole numbers, integers and rational numbers make up the irrational numbers.
   • Irrational numbers make up all the real numbers.
9. 8.

   Kira says √26 is irrational. Which reason is best?

   • 26 is not a perfect square, so the decimal never ends or repeats.
   • 26 is a big number, so √26 must be irrational.
   • 26 is not a perfect square, so the decimal stops after a few digits.
   • √26 has a root sign, and every square root is irrational.

10. Use this

    Number line from 0 to 2, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers.

11. 9.

    Luz says 0.2727… is rational. Which reason is best?

    • Its digits go on forever, so it cannot be a fraction.
    • All decimals are rational.
    • It is less than 1, so it is rational.
    • The block 27 repeats, so it can be written as a fraction.

12. Use this

    Number line from 0 to 5, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers.

13. 10.

    Milo says π is irrational. Which reason is best?

    • π is a circle number, so it cannot be real.
    • π equals 3.14, which stops, so it is a fraction.
    • π = 3.1415926… and its digits never end or repeat.
    • π equals 22/7, so it is a fraction.