Compare and order real numbers

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. Read this first

   Use this

   Number line with a tick at every hundredth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Card A is √14, card B is 3 4/5, card C is 3.6, card D is 365%, card E is 3.7.

2. 1.

   Tala deals five number cards. Which order, from least to greatest, is right? Write the five letters.

   C, D, E, A, B

3. Use this

   Number line with a tick at every hundredth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Card A is π, card B is 22/7, card C is 3.1, card D is 3.2, card E is √10.

4. 2.

   Zee ranks five cards, two of them close to π. Which order, from greatest to least, is right? Write the five letters.

   D, E, B, A, C

5. Use this

   Number line with a tick at every hundredth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Card A is √2, card B is 1 2/5, card C is 142%, card D is 1.41, card E is 1.45.

6. 3.

   Ari sorts five number cards for a game. Which order, from least to greatest, is right? Write the five letters.

   B, D, A, C, E

7. Use this

   Number line with a tick at every thousandth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Card A is 7.2 × 10⁻¹, card B is 3/4, card C is 70%, card D is 0.073.

8. 4.

   Jun ranks four number cards. Which order, from greatest to least, is right? Write the four letters.

   B, A, C, D
9. 5.

   Kira looks for numbers in a gap on the number line. Which pair has one rational and one irrational number, both between 4 and 5?

   • 4.5 and √30
   • 4.2 and 4.8
   • √17 and √21
   • 4.5 and √18
10. 6.

    Luz picks two numbers between two whole numbers. Which pair has one rational and one irrational number, both between 2 and 3?

    • 2.5 and √12
    • √5 and √8
    • 2.2 and 2.7
    • 2.5 and √7
12. 7.

    Pia checks a cube root against a decimal. Which is greater, ∛20 or 2.8?

    • ∛20 is greater.
    • 2.8 is greater.
    • They are equal.
13. 8.

    Ren tests a cube root against a decimal. Which is greater, ∛100 or 4.5?

    Use the picture in question 7.

    • 4.5 is greater.
    • They are equal.
    • ∛100 is greater.
14. 9.

    Tala explains a comparison on the board. Which reason shows that √50 is greater than 7?

    Use the picture in question 7.

    • 7 × 7 = 49, and 50 is more than 49.
    • A root sign makes a number bigger.
    • √50 is about 5.
    • 50 is greater than 7.
15. 10.

    Zee defends a comparison in math club. Which reason shows that √40 is less than 6.5?

    Use the picture in question 7.

    • A root is always smaller than a plain number.
    • √40 is about 7.
    • 40 is much bigger than 6.5.
    • 6.5 × 6.5 = 42.25, and 40 is less than 42.25.