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 4.2 × 10⁻¹, card B is 0.04, card C is 1/2, card D is 41%.

8. 4.

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

   B, D, A, C

9. 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 3.5 × 10⁻², card B is 3/10, card C is 0.4%, card D is 2.5%.

10. 5.

    Esme lines up four cards. Which order, from least to greatest, is right? Write the four letters.

    C, D, A, B
11. 6.

    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
    • 4.5 and √18
    • √17 and √21
    • 4.2 and 4.8
12. 7.

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

    • 2.2 and 2.7
    • √5 and √8
    • 2.5 and √7
    • 2.5 and √12
13. 8.

    Milo searches for numbers between 7 and 8. Which pair has one rational and one irrational number, both between 7 and 8?

    • √52 and √60
    • 7.5 and √40
    • 7.2 and 7.8
    • 7.5 and √56
15. 9.

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

    • A root sign makes a number bigger.
    • √50 is about 5.
    • 7 × 7 = 49, and 50 is more than 49.
    • 50 is greater than 7.
16. 10.

    Ari checks a reason for a comparison. Which reason shows that √90 is greater than 9.4?

    Use the picture in question 9.

    • Roots are always smaller than plain numbers.
    • 9.4 × 9.4 = 88.36, and 90 is more than 88.36.
    • 90 is greater than 9.4.
    • √90 is about 10.