Section C Section C Checkpoint

Problem 1

For each pair, determine which quantity is larger, and estimate how many times larger.

    1. The country of Canada covers approximately 10 million square kilometers.
    2. The country of Mexico covers approximately 2⋅1062\boldcdot10^6 square kilometers.
    1. The diameter of one atom of hydrogen is 5⋅10-115\boldcdot10^{\text-11} meters.
    2. The diameter of one atom of magnesium is 3⋅10-103\boldcdot10^{\text-10} meters.
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Solution
  1. The country of Canada covers an area about 5 times the size of the country of Mexico, because 10,000,000=10⋅10610,000,000=10\boldcdot10^6, which is 5 times larger than 2⋅1062\boldcdot10^6.
  2. The diameter of one atom of magnesium is 6 times larger than the diameter of one atom of hydrogen, because 3⋅10-10=30⋅10-113\boldcdot10^{\text-10}=30\boldcdot10^{\text-11}, which is 6 times larger than 5⋅10-115\boldcdot10^{\text-11}
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Sample Response
  1. The country of Canada covers an area about 5 times the size of the country of Mexico, because 10,000,000=10⋅10610,000,000=10\boldcdot10^6, which is 5 times larger than 2⋅1062\boldcdot10^6.
  2. The diameter of one atom of magnesium is 6 times larger than the diameter of one atom of hydrogen, because 3⋅10-10=30⋅10-113\boldcdot10^{\text-10}=30\boldcdot10^{\text-11}, which is 6 times larger than 5⋅10-115\boldcdot10^{\text-11}

Problem 2

Fingernails grow at a rate of about 10-910^{\text-9} meters per second. How long would it take a fingernail to grow 1 centimeter? Explain or show your reasoning.
(There are 100 centimeters in 1 meter.)
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Solution
10710^7 or 10,000,000 seconds (about 166,667 minutes or 2,778 hours or 115 days or almost 4 months). Sample reasoning: Since a fingernail grows 10-910^{\text-9} meter per second, it will take 10910^9 seconds to grow 1 meter. Since there are 100 or 10210^2 centimeters in 1 meter, 109102=107\frac{10^9}{10^2}=10^7.
Show Sample Response
Sample Response
10710^7 or 10,000,000 seconds (about 166,667 minutes or 2,778 hours or 115 days or almost 4 months). Sample reasoning: Since a fingernail grows 10-910^{\text-9} meter per second, it will take 10910^9 seconds to grow 1 meter. Since there are 100 or 10210^2 centimeters in 1 meter, 109102=107\frac{10^9}{10^2}=10^7.