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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.

Arizona Academic Standards 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 Arizona

In the Arizona Academic Standards, 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: Arizona 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

    Use mental math. What is 387 ÷ 100?

    387 ÷ 100 = ?

    answer box

  2. Question 2

    Tap the numbers from least to greatest.

    • √5
    • −1.5
    • √10
    • √2

  3. Question 3

    Write 6100 in scientific notation (a number from 1 up to 10, times a power of 10).

    • 6.1 × 10³
    • 6.1 × 10²
    • 6.1 × 10⁴
    • 61 × 10²

  4. Question 4

    Every integer is…

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

  5. Question 5

    Which number is equal to 7.3 × 10⁸?

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

  6. Question 6

    Which number is irrational?

    • −3/4
    • √100
    • √5
    • 1.5

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