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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.

Alabama Course of Study content standard: 8.1; 8.2; 8.5; 8.6 · 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 Alabama

In the Alabama Course of Study, 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: Alabama State Department of Education (ALSDE)

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 1.9 × 10⁻⁴?

    • 0.0019
    • 19,000
    • 0.00019
    • 0.000019

  2. Question 2

    Use mental math. What is 3.40 × 10?

    3.40 × 10 = ?

    answer box

  3. Question 3

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

    • the distance light travels in a year, in meters
    • the width of a pencil, in meters
    • the thickness of a soap bubble, in meters
    • the mass of a grain of sand, in kilograms

  4. Question 4

    Which is the greatest number?

    • 1.2 × 10⁶
    • 6.1 × 10⁻⁴
    • 7.3 × 10⁸

  5. Question 5

    Tap the numbers from least to greatest.

    • √10
    • π
    • −1.5
    • −√5

  6. Question 6

    Every integer is…

    • an irrational number
    • a negative number
    • a decimal that never ends
    • a rational number

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