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Chapter 1, Problem 1.1P

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Chemistry (7th Edition)

7th Edition
John E. McMurry + 2 others
ISBN: 9780321943170

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Chapter
Section
BuyFindarrow_forward

Chemistry (7th Edition)

7th Edition
John E. McMurry + 2 others
ISBN: 9780321943170
Interpretation Introduction

To determine:

The scientific notation of following quantities and to express the number and unit with the most appropriate prefix.

  • The diameter of an insulin molecule, 0.000000005m
  • The circumference of the earth at the equator, 40075017m
  • Answer

    Solution:

  • 5×109m,5nm
  • 4.0075017×106m,40.075017Mm
  • Explanation

    The best way to write any scientific notation is in the form of N×10a. Here, N is a number between 1 and 10 and “a” is an exponent.

    The prefix multipliers are the fixed numeral values used in SI system to reduce the difficulties in measurement. For example, one nanometer: 1nm=10-9m , here “nano” is a prefix used for a value of 10-9.

    Given:

    1. The diameter of an insulin molecule, 0.000000005m
    Step 1: To write the given value in scientific notation, the decimal should be shifted right to find a value of N and an exponent for 10.

    The value becomes as: 0.000000005m=5×109m

    Step2: The unit “meter” is written with proper prefix as follows:

    Since, 1nm=109m

    Hence,

      5×109m=1nm 10 9m×5×109m=5nm

     b. The circumference of the earth at the equator, 40075017m

    Step 1: To write the given value in scientific notation, the above value should be converted into decimal form to find a value of N and an exponent for 10.

    The value becomes as:

      40075017mm=4.0075017×107m

    Step2: The unit “meter” is written with proper prefix as follows:

    Since, the prefix mega (M) has the value of 1Mm=106m

    Now, the value of circumference should be converted to the comparative value as:

      4.0075017×107m=40.075017×106m

    Hence,

      40.075017×106m=1Mm 10 6m×40.075017×106m=40.075017Mm

    Conclusion
    1. The diameter of an insulin molecule, 0.000000005m is represented as 5×109m,5nm.
    2. The circumference of the earth at the equator, 40075017m is represented as 4.0075017×106m,40.075017Mm.

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