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8th grade · Math · Unit 1 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.2(A); 8.2(C); 8.2(D) · sets of real numbers, scientific notation, and ordering real numbers

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 1 of 15 in 8th grade Math, before Squares, Cubes & Roots.

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: Texas Education Agency (TEA)

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 24.8 ÷ 100?

    24.8 ÷ 100 = ?

    answer box

  2. Question 2

    Use mental math. What is 792 ÷ 100?

    792 ÷ 100 = ?

    answer box

  3. Question 3

    Tap the numbers from least to greatest.

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

  4. Question 4

    Which number is equal to 6.1 × 10⁶?

    • 610,000
    • 61,000,000
    • 610,000,000
    • 6,100,000

  5. Question 5

    Write 25,000 in scientific notation (a number from 1 up to 10, times a power of 10).

    • 2.5 × 10⁴
    • 25 × 10³
    • 2.5 × 10⁵
    • 2.5 × 10³

  6. Question 6

    Which number is rational?

    • √49
    • π
    • √11
    • √5

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