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 π, card B is 22/7, card C is 3.1, card D is 3.2, card E is √10.

2. 1.

   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

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 √2, card B is 1 2/5, card C is 142%, card D is 1.41, card E is 1.45.

4. 2.

   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

5. 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%.

6. 3.

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

   B, D, A, C

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

8. 4.

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

   C, D, A, B
9. 5.

   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
11. 6.

    Noah compares a cube root with a decimal. Which is greater, ∛30 or 3.2?

    • 3.2 is greater.
    • ∛30 is greater.
    • They are equal.
12. 7.

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

    Use the picture in question 6.

    • They are equal.
    • 4.5 is greater.
    • ∛100 is greater.
13. 8.

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

    Use the picture in question 6.

    • 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.
14. 9.

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

    Use the picture in question 6.

    • √40 is about 7.
    • 40 is much bigger than 6.5.
    • 6.5 × 6.5 = 42.25, and 40 is less than 42.25.
    • A root is always smaller than a plain number.
15. 10.

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

    Use the picture in question 6.

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