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8th grade · Math · Unit 5 of 17

Big, Small & Real Numbers

Scientific notation and irrational numbers

What your child practices

Writing very large and very small numbers in scientific notation, telling rational from irrational numbers, ordering numbers such as √2 and π, and mentally multiplying and dividing by powers of ten.

Maine Learning Results learning standard: 8.NS.A.1; 8.NS.A.2; 8.EE.A.3; 8.EE.A.4 · irrational numbers and scientific notation

How we explain it

Children can open this short lesson before they practice.

  1. Scientific notation writes a number as a number from 1 to 10 times a power of 10.
  2. Multiplying by 10³ moves the decimal point 3 places right.
  3. Irrational numbers, like π, cannot be written as a fraction.

Example: Write 45,000 in scientific notation. Move the point 4 places left: 4.5. So 45,000 = 4.5 × 10⁴. Answer: 4.5 × 10⁴

Big, Small & Real Numbers in Maine

In the Maine Learning Results, this is unit 5 of 17 in 8th grade Math, after Surface Area & Volume and before Scatter Plots & Stories.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Maine Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Which number is equal to 7.3 × 10⁸?

    • 73,000,000,000
    • 7,300,000,000
    • 73,000,000
    • 730,000,000

  2. Question 2

    Which statement is true?

    • All rational numbers and all irrational numbers are real numbers.
    • Irrational numbers are rational numbers.
    • A number can be both rational and irrational.
    • Real numbers are only whole numbers.

  3. Question 3

    Which is the greatest number?

    • 4.7 × 10⁻⁸
    • 9.5 × 10⁹
    • 3.6 × 10⁸

  4. Question 4

    Tap the numbers from least to greatest.

    • π
    • √10
    • 1.5
    • √2

  5. Question 5

    Which quantity is most likely written with a negative exponent in scientific notation?

    • the mass of Earth, in kilograms
    • the distance from Earth to the Sun, in meters
    • the width of a human hair, in meters
    • the number of people in Canada

  6. Question 6

    Use mental math. What is 0.256 × 10,000?

    0.256 × 10000 = ?

    answer box

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