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8th grade · Math · Unit 4 of 11

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.

Minnesota K-12 Academic Standards benchmark: 8.3.5.1; 8.3.5.4 · 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 Minnesota

In the Minnesota K-12 Academic Standards, this is unit 4 of 11 in 8th grade Math, after Pythagorean Theorem 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: Minnesota Department of Education (MDE)

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 rational?

    • √11
    • π
    • √13
    • −3/4

  2. Question 2

    Write 0.00056 in scientific notation (a number from 1 up to 10, times a power of 10).

    • 56 × 10⁻⁵
    • 5.6 × 10⁴
    • 5.6 × 10⁻³
    • 5.6 × 10⁻⁴

  3. Question 3

    Which statement is true?

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

  4. Question 4

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

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

  5. Question 5

    Tap the numbers from least to greatest.

    • √2
    • √10
    • π
    • −1.5

  6. Question 6

    Which number is equal to 8.4 × 10⁻²?

    • 840
    • 0.84
    • 0.084
    • 0.0084

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