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Standard form: A × 10ⁿ

Mathematics · Number Representation & Place Value · ages 12-14
Name ______________________   Date ____________

  1. In 5.2 × 10³, what does the exponent 3 tell you when you convert back to an ordinary number?

    • Multiply 5.2 by 3, giving 15.6
    • Move the point 3 places right, giving 5,200
    • Move the point 3 places left, giving 0.0052

  2. Moving the decimal point in 0.000508 four places right gives 5.08. Which factor must multiply 5.08 to restore the original value?

    • 10⁴
    • 10⁻⁴
    • 10⁻⁵
    • 10⁵

  3. Write 3.6 × 10⁻² as an ordinary number.

    Answer: ______________

  4. Which of these is correctly written in standard form?

    • 3.4 × 10⁶
    • 34 × 10⁵
    • 0.34 × 10⁷

  5. Which number is largest?

    • 8.1 × 10⁻⁴
    • 8.4 × 10⁻⁴
    • 8.7 × 10⁻⁴
    • 8.2 × 10⁻⁴

  6. Which number is larger: 3 × 10⁵ or 7 × 10⁴?

    • 3 × 10⁵
    • 7 × 10⁴
    • They are equal

  7. How much larger is 7.2 × 10⁵ than 3.2 × 10⁵? Give the difference as an ordinary number.

    Answer: ______________

  8. Write 62,000 in standard form.

    • 6.2 × 10³
    • 62 × 10³
    • 6.2 × 10⁴

  9. A sensor records a length as 0.0068 × 10² m. Which expression gives the same length in standard form?

    • 6.8 × 10¹ m
    • 6.8 × 10⁻¹ m
    • 6.8 × 10⁻⁵ m

  10. One sample has mass 4.8 × 10⁻³ g. Another has mass 1.2 × 10⁻⁴ g. How many times as large is the first mass as the second?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Standard form: A × 10ⁿ W1-mt_bO-njVOige-s1

  1. Move the point 3 places right, giving 5,200 · The exponent tells you how many places to move the decimal point. A positive exponent moves it right.
  2. 10⁻⁴ · Restoring the original value requires four divisions by 10. The factor is 10⁻⁴, so 0.000508 = 5.08 × 10⁻⁴.
  3. 0.036 · 3.6 × 10⁻² = 3.6 ÷ 100 = 0.036.
  4. 3.4 × 10⁶ · In standard form, A must be at least 1 and less than 10. 34 and 0.34 are outside that range.
  5. 8.7 × 10⁻⁴ · The exponents match, so compare the coefficients. The largest coefficient is 8.7.
  6. 3 × 10⁵ · 3 × 10⁵ is 300,000 and 7 × 10⁴ is 70,000, so the larger exponent wins here.
  7. 400000 · 720,000 - 320,000 = 400,000.
  8. 6.2 × 10⁴ · Moving the decimal point in 6.2 4 places right gives 62,000, so the exponent is 4.
  9. 6.8 × 10⁻¹ m · Multiply the coefficient by 10 three times and lower the exponent three times: 0.0068 × 10² = 6.8 × 10⁻¹ = 0.68.
  10. 40 · The masses are 0.0048 g and 0.00012 g. Their ratio is 0.0048 ÷ 0.00012 = 480 ÷ 12 = 40.
Worksheet · LightMySky