Chapter 1, Problem 1.1P

Express the diameter of a nanoparticle(0.000 000 050 m) in scientific notation, and then express the number and unit with the most appropriate prefix.

Interpretation Introduction

Interpretation:

The diameter of the nanoparticle in scientific notation with number and unit in most appropriate prefix is to be expressed.

Concept introduction:

The size of the units on any system of measurement can be inconveniently very large or small. To solve this problem, SI units are modified by use of some appropriate prefixes that are placed before the units to signify how small or big the size of the unit is. For example, the prefix milli is used to represent one-thousandth of 1 meter.

Similarly, numbers that are too large or too small are represented by an exponential format called scientific notations for convenience.

Scientific notations are generally expressed as follows:

$\text{m}{\text{×10}}^{\text{n}}$

Where,

• n is the number of places the decimal has moved and is known as an exponent.
• m is the number.

An example is 55000 is represented as $5.5\times {10}^4$.

Answer to Problem 1.1P

The scientific notation for $\text{0}\text{.000000050}\text{m}$ is $5.0\times {10}^{-8}\text{m}$ and the number and unit with the most appropriate prefix will be $50\text{nm}$.

Explanation of Solution

Given information:

The diameter of the nanoparticle is $\text{0}\text{.000000050}\text{m}$

To assign scientific notation( $\text{m}{\text{×10}}^{\text{n}}$ ),

• The decimal point is moved to either right or left until a number is obtained that lies between 1 to 10.
• If the decimal is moved to the right, then the exponent is negative and if the decimal is moved to left then the exponent is positive.
• Select an appropriate prefix that is close to the exponent.

The scientific notation for $\text{0}\text{.000000050}\text{m}$ can be written by shifting the decimal 8 places to the right. So the exponent (n) will be $-8$ and the scientific notation becomes $5.0\times {10}^{-8}\text{m}$.

The appropriate prefix that is close to the exponent will be Nano. Nano is equal to 0.000000001 and in the scientific exponent, it will be ${10}^{-9}$. So the number and unit with the most appropriate prefix will be $50\text{nm}$.

Conclusion

The scientific notation for $\text{0}\text{.000000050}\text{m}$ is $5.0\times {10}^{-8}\text{m}$ and the number and unit with the most appropriate prefix will be $50\text{nm}$.