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8th grade · Math · Unit 1 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.

Washington State Learning Standards learning standard: M.8.Q.NS.1; M.8.Q.NS.2; M.8.Q.EE.3; M.8.Q.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

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?

    • √7
    • −3/4
    • √2
    • √5

  2. Question 2

    Write 0.056 in scientific notation (a number from 1 up to 10, times a power of 10).

    • 5.6 × 10⁻¹
    • 56 × 10⁻³
    • 5.6 × 10⁻²
    • 5.6 × 10²

  3. Question 3

    A scientist writes 6.02 × 10²³. What does the exponent 23 tell you?

    • The number has 23 digits before the decimal point.
    • The decimal point moves 23 places to the right.
    • The decimal point moves 23 places to the left.
    • Multiply 6.02 by 23.

  4. Question 4

    Which is the least number?

    • 3.6 × 10²
    • 3.2 × 10⁴
    • 6.1 × 10⁻⁶

  5. Question 5

    Use mental math. What is 0.596 × 1000?

    0.596 × 1000 = ?

    answer box

  6. Question 6

    Use mental math. What is 0.63 × 10?

    0.63 × 10 = ?

    answer box

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