Kinds of real numbers: rational and irrational

Grade 8 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Bo copies a long decimal into a notebook. Point P is the number 2.1666…, and its digits repeat the digit 6 forever. What is the smallest group that holds P?

   • integers
   • rational numbers
   • irrational numbers
2. 2.

   Esme types a measurement into a calculator. Point P is the number 3.75, and its digits stop after the 5. What is the smallest group that holds P?

   • irrational numbers
   • integers
   • rational numbers
3. 3.

   Kira presses the square root key and sees a long string of digits. Point P is the number 1.4142135…, and its digits never end and never repeat. What is the smallest group that holds P?

   • irrational numbers
   • integers
   • rational numbers, because it is a decimal
4. 4.

   Luz scrolls through a screen full of digits. Point P is the number 2.6457513…, and its digits never end and never repeat. What is the smallest group that holds P?

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

   Milo writes 6.0 in a score box. Point P is the number 6.0, and its digits are a 6, a point and a 0, and nothing more. What is the smallest group that holds P?

   • irrational numbers
   • whole numbers
   • integers
   • rational numbers
6. 6.

   Noah puts √49 on a number line for a poster. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √49?

   • irrational numbers
   • rational numbers
   • whole numbers
7. 7.

   Pia wants to place √20 on a number line. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √20?

   • irrational numbers
   • whole numbers
   • rational numbers

8. Read this first

   Use this

   Number line from 0 to 13, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Check: 12 × 12 = 144. P is the mark √144.

9. 8.

   Ren is checking √144 for a puzzle. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √144?

   • irrational numbers
   • whole numbers
   • rational numbers
10. 9.

    Tala marks √12 on a chalk number line. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √12?

    • whole numbers
    • irrational numbers
    • rational numbers
11. 10.

    Bo finds √90 in a math game. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √90?

    • rational numbers
    • whole numbers
    • irrational numbers