Compare and order real numbers

Grade 8 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ari compares two lengths on a ruler strip. The figure gives the decimal for √12. Which is greater, √12 or 3.6?

   • 3.6 is greater.
   • √12 is greater.
   • They are equal.

2. Read this first

   Use this

   Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. √30 ≈ 5.48.

3. 2.

   Bo checks a root against a decimal. The figure gives the decimal for √30. Which is greater, √30 or 5.4?

   • √30 is greater.
   • 5.4 is greater.
   • They are equal.

4. Use this

   Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. √8 ≈ 2.83.

5. 3.

   Kira sorts two number cards. The figure gives the decimal for √8. Which is greater, √8 or 2.9?

   • They are equal.
   • √8 is greater.
   • 2.9 is greater.
6. 4.

   Luz decides which card is greater. The figure gives the decimal for √17. Which is greater, √17 or 4.0?

   • They are equal.
   • √17 is greater.
   • 4.0 is greater.
7. 5.

   Milo compares a root with a decimal. The figure gives the decimal for √26. Which is greater, √26 or 5.2?

   • They are equal.
   • 5.2 is greater.
   • √26 is greater.

8. Use this

   Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. √36 = 6.

9. 6.

   Noah checks two cards that look different. The figure gives the decimal for √36. Which is greater, √36 or 6.0?

   • 6.0 is greater.
   • √36 is greater.
   • They are equal.
10. 7.

    Pia puts three numbers on cards in a row. The figure gives each decimal. Which list is in order from least to greatest?

    • 2.3, 9/4, √5
    • √5, 9/4, 2.3
    • 9/4, 2.3, √5
    • 9/4, √5, 2.3
11. 8.

    Number line with a tick at every tenth. Ren lines up three cards on a desk. The figure gives each decimal. Which list is in order from least to greatest?

    • 10/3, 3.4, √11
    • 3.4, 10/3, √11
    • 10/3, √11, 3.4
    • √11, 10/3, 3.4

12. Use this

    Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Decimals: √7 ≈ 2.65, 2.6, 8/3 ≈ 2.67.

13. 9.

    Tala sorts three number cards. The figure gives each decimal. Which list is in order from greatest to least?

    • 2.6, √7, 8/3
    • 8/3, √7, 2.6
    • √7, 8/3, 2.6
14. 10.

    Ari orders three cards, one with a circle number. The figure gives each decimal. Which list is in order from least to greatest?

    • 22/7, π, 3.1
    • 3.1, π, 22/7
    • π, 3.1, 22/7