# Chapter 1, Problem 1.1P

### Chemistry (7th Edition)

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

Chapter
Section

### 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

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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