Scientific Notation in Chemistry: Writing and Interpreting Numbers

Chapter 1: Chemistry in Our Lives

Introduction to Scientific Notation

In chemistry, we often encounter extremely large or small numbers, such as the number of atoms in a sample or the width of microscopic objects. Scientific notation is a standardized way to express these numbers, making calculations and comparisons easier.

• Scientific notation expresses numbers as a product of a coefficient and a power of ten.

• This notation is essential for clarity and efficiency in scientific communication.

Writing Numbers in Scientific Notation

To write a number in scientific notation, follow these steps:

1. Move the decimal point in the number to create a new number from 1 up to (but not including) 10. This new number is called the coefficient.

2. Count how many places you moved the decimal point. This number becomes the exponent of 10.

3. If you moved the decimal to the left, the exponent is positive. If you moved it to the right, the exponent is negative.

4. Write the number as: coefficient × 10exponent.

Example: The width of a human hair is 0.000008 m. In scientific notation, this is written as $8 \times 10^{-6}$ m.

Example: The average number of hairs on a human scalp is 100,000. In scientific notation, this is $1 \times 10^{5}$ hairs.

Structure of Scientific Notation

Numbers in scientific notation have two parts:

• Coefficient: A number at least 1 but less than 10.

• Power of 10: An integer exponent indicating how many places the decimal point was moved.

General form:

$a \times 10^{n}$

• a is the coefficient ($1 \leq a < 10$)

• n is an integer (positive for large numbers, negative for small numbers)

Example: $1.5 \times 10^{2}$ (where 1.5 is the coefficient and 2 is the exponent)

Converting Standard Numbers to Scientific Notation

• Move the decimal point to create a coefficient between 1 and 10.

• Count the number of places moved to determine the exponent.

• Write the number as the product of the coefficient and the appropriate power of 10.

Examples:

Standard Number	Scientific Notation
2,400	$2.4 \times 10^{3}$
0.000086	$8.6 \times 10^{-5}$

Comparing Numbers in Standard and Scientific Notation

Scientific notation allows for easy comparison of very large and very small numbers. For example:

Quantity	Standard Format	Scientific Notation
Diameter of the Earth	12,800,000 m	$1.28 \times 10^{7}$ m
Mass of a human	68,000 g	$6.8 \times 10^{4}$ g
Diameter of a chickenpox virus	0.0000003 cm	$3 \times 10^{-7}$ cm

Using Scientific Notation on Calculators

Most scientific calculators use the EE or EXP key to enter numbers in scientific notation. The display may show numbers in the form of "E" notation, where "E" stands for "exponent." For example:

• $4.05 \times 10^{6}$ may be displayed as 4.05E6

• $2.5 \times 10^{-4}$ may be displayed as 2.5E-4

Always interpret the calculator display correctly when recording scientific data.

Practice: Writing Numbers in Scientific Notation

To convert 6,400 to scientific notation:

1. Move the decimal point three places to the left: 6.4

2. Write as $6.4 \times 10^{3}$

To convert 0.000021 to scientific notation:

1. Move the decimal point five places to the right: 2.1

2. Write as $2.1 \times 10^{-5}$

Summary Table: Scientific Notation Conversion

Standard Number	Scientific Notation
0.000008	$8 \times 10^{-6}$
7,200,000	$7.2 \times 10^{6}$

Concept Map: Chemistry in Our Lives

Chemistry is a central science that connects to many aspects of our daily lives, from the composition of hair to the structure of viruses. Understanding scientific notation is a foundational skill for studying chemistry and interpreting scientific data.