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Grade 8 · Math

8th grade Compare and order real numbers worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Compare and order real numbers

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  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. 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. √45 ≈ 6.71.

  5. Esme marks two numbers on a chalk line. The figure gives the decimal for √45. Which is greater, √45 or 6.5?

    • 6.5 is greater.
    • They are equal.
    • √45 is greater.

  6. Jun tests two numbers on a poster line. The figure gives the decimal for √20. Which is greater, √20 or 4.6?

    • 4.6 is greater.
    • They are equal.
    • √20 is greater.

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

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

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

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

  9. 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.

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

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

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

  12. Zee orders three numbers for a game. The figure gives each decimal. Which list is in order from least to greatest?

    • 7/4, √3, 1.7
    • 1.7, 7/4, √3
    • 1.7, √3, 7/4
    • √3, 1.7, 7/4

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

    • π, 3.1, 22/7
    • 3.1, π, 22/7
    • 22/7, π, 3.1
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8th grade Compare and order real numbers worksheet – printable
Print: 123456

About this worksheet

Compare and order real numbers. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can say which is greater, a root or a number in another form, by squaring the other number and comparing it with the number under the root.
  • I can write five numbers in order, changing each into a decimal first: roots, π, fractions, mixed numbers, percents and powers of ten.
  • I can explain why a comparison is true, and name a rational and an irrational number between two numbers.

Standard: 8.NS.A.2

Words to know

greater: Farther right on the number line.

least to greatest: From the number farthest left to the number farthest right.

square a number: Multiply it by itself: 3.6 squared is 3.6 × 3.6 = 12.96.

cube a number: Multiply it by itself three times: 3.2 cubed is 3.2 × 3.2 × 3.2.

scientific notation: A number times a power of ten: 4.2 × 10⁻¹ is 0.42.

between: Greater than one number and less than the other.

Common mistakes

Your child used the number under the root sign as the size of the root.

Your child thought a root is always the smaller number.

Your child ignored the percent sign.

What to say

Ask: what is the square root of 25? Is it 25?

Ask: is the square root of 30 bigger or smaller than 5?

Ask: what is 270% as a decimal? Is it near 270 or near 2.7?

Questions parents ask

What is the most common mistake with compare and order real numbers?

Your child used the number under the root sign as the size of the root.

How can I help my child with compare and order real numbers?

Ask: what is the square root of 25? Is it 25?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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