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The Apprentice’s Guide to Physics: An Introductory Quest Through the Mechanics of the Universe

M. E. Spellwing

Section 1.3 Practice

Subsection 1.3.1 Practice: Scientific Notation

Extra questions to help level up your abilities.

Checkpoint 1.3.1.

    The average distance from Earth to Pluto is about \(5900000000\) meters. Convert \(5900000000\) to scientific notation.
  • \(5.9 \times 10^9\)
  • Correct! \(5900000000 = 5.9 \times 10^9\)
  • \(59 \times 10^8\)
  • Try again. While \(59 \times 10^8 = 5900000000\text{,}\) the coefficient must be greater than or equal to \(1\) and less than \(10\) for scientific notation.
  • \(5.9 \times 10^{-9}\)
  • Try again. The decimal moved left, so the power should be positive.
  • \(5.9 \times 10^8\)
  • Try again. Try counting the decimal places again.

Checkpoint 1.3.2.

    The distance from Earth to the nearest star (Proxima Centauri) is about \(40200000000000\) meters. Convert \(40200000000000\) to scientific notation.
  • \(4.02 \times 10^{13}\)
  • Correct! \(40200000000000 = 4.02 \times 10^{13}\)
  • \(402 \times 10^{11}\)
  • Try again. While \(402 \times 10^{11} = 40200000000000\text{,}\) the coefficient must be greater than or equal to \(1\) and less than \(10\) for scientific notation.
  • \(4.02 \times 10^{-13}\)
  • Try again. The decimal moved left, so the power should be positive.
  • \(4.02 \times 10^{11}\)
  • Try again. Try counting the decimal places again.

Checkpoint 1.3.3.

    The distance from the Milky Way to the Andromeda Galaxy is about \(2500000000000000000\) meters. Convert \(2500000000000000000\) to scientific notation.
  • \(2.5 \times 10^{18}\)
  • Correct! \(2500000000000000000 = 2.5 \times 10^{18}\)
  • \(25 \times 10^{17}\)
  • Try again. While \(25 \times 10^{17} = 2.5 \times 10^{18}\text{,}\) the coefficient must be greater than or equal to \(1\) and less than \(10\) for scientific notation.
  • \(2.5 \times 10^{-18}\)
  • Try again. The decimal moved left, so the power should be positive.
  • \(2.5 \times 10^{17}\)
  • Try again. Try counting the decimal places again.

Checkpoint 1.3.4.

    The diameter of a hydrogen atom is about \(5.3 \times 10^{-11}\) meters. Convert \(5.3 \times 10^{-11}\) to standard decimal notation.
  • \(0.000000000053\)
  • Correct! \(5.3 \times 10^{-11} = 0.000000000053\)
  • \(0.0000000053\)
  • Try again. You only moved the decimal \(9\) places instead of \(11\text{.}\)
  • \(530000000000\)
  • Try again. Recall that if the exponent is negative the decimal should move to the left.
  • \(0.000000000000053\)
  • Try again. That’s one place too far! The exponent is \(-11\text{,}\) not \(-13\text{.}\)

Checkpoint 1.3.5.

    The Planck length
     1 
    simple.wikipedia.org/wiki/Planck_length
    is approximately \(1.6 \times 10^{-35}\) meters. Convert \(1.6 \times 10^{-35}\) to standard decimal notation.
  • \(0.000000000000000000000000000000000016\)
  • Correct! \(1.6 \times 10^{-35} = 0.000000000000000000000000000000000016\)
  • \(0.00000000000000000000000016\)
  • Try again. You only moved the decimal \(25\) places instead of \(35\text{.}\)
  • \(160000000000000000000000000000000000\)
  • Try again. Recall that if the exponent is negative the decimal should move to the left.
  • \(0.0000000000000000000000000000000000000000016\)
  • Try again. That’s \(42\) places, we see what you did there. Try again.

Checkpoint 1.3.6.

    About how many orders of magnitude larger is the distance from Milky Way to Andromeda Galaxy compared to the distanced from Earth to Proxima Centauri? Use questions Checkpoint 1.3.2 and Checkpoint 1.3.3 to help.
  • \(5\)
  • Correct! \(18-13=5\) orders of magnitude.
  • \(31\)
  • Try again. You added the exponents, try subtracting.
  • \(1.38\)
  • Try again. You divided the exponents, try subtracting.
  • \(0.722\)
  • Try again. You divided the exponents, try subtracting.
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