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8th grade · Math · Unit 5 of 19

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.

New York State Learning Standards learning standard: NY-8.NS.1; NY-8.NS.2; NY-8.EE.3; NY-8.EE.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 New York

In the New York State Learning Standards, this is unit 5 of 19 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: New York State Education Department (NYSED)

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 describes 0.333… (the 3 repeats forever)?

    • an integer
    • not a real number
    • rational, because it equals 1/3
    • irrational, because it never ends

  2. Question 2

    Which number is equal to 4.7 × 10⁵?

    • 47,000
    • 47,000,000
    • 4,700,000
    • 470,000

  3. Question 3

    Tap the numbers from least to greatest.

    • −√3
    • √10
    • π
    • 3.2

  4. Question 4

    Write 950,000 in scientific notation (a number from 1 up to 10, times a power of 10).

    • 95 × 10⁴
    • 9.5 × 10⁶
    • 9.5 × 10⁵
    • 9.5 × 10⁴

  5. Question 5

    Use mental math. What is 0.661 × 100?

    0.661 × 100 = ?

    answer box

  6. Question 6

    Which is the least number?

    • 5.6 × 10²
    • 9.5 × 10⁻⁴
    • 4.7 × 10⁻⁸

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