BackScientific Notation in Chemistry: Chapter 1 Study Notes
Study Guide - Smart Notes
Tailored notes based on your materials, expanded with key definitions, examples, and context.
Chapter 1: Chemistry in Our Lives
Introduction to Scientific Notation
Scientific notation is a method used in chemistry and other sciences to express very large or very small numbers in a concise and standardized format. This is especially useful when dealing with measurements and quantities that span many orders of magnitude.
Scientific notation expresses numbers as a product of a coefficient and a power of ten.
The coefficient is a number equal to or greater than 1 but less than 10.
The power of ten indicates how many places the decimal point has been moved.
Example: The average number of hairs on a human scalp is about . The diameter of a hair is about meters.
Writing Numbers in Scientific Notation
To convert a standard number to scientific notation, follow these steps:
Move the decimal point to create a coefficient between 1 and 10.
Count the number of places the decimal point was moved; this becomes the exponent of 10.
If the decimal is moved to the left, the exponent is positive; if to the right, the exponent is negative.
Example:
2400 in scientific notation: Move the decimal 3 places left to get 2.4. The exponent is 3.
0.00086 in scientific notation: Move the decimal 4 places right to get 8.6. The exponent is -4.
Table: Powers of Ten and Scientific Notation
The following table summarizes how standard numbers are represented in scientific notation using powers of ten:
Standard Number | Multiples of 10 | Scientific Notation | Description |
|---|---|---|---|
10,000 | 10 × 10 × 10 × 10 | Positive power of ten | |
1,000 | 10 × 10 × 10 | Positive power of ten | |
100 | 10 × 10 | Positive power of ten | |
10 | 10 | Positive power of ten | |
1 | 0 | Zero power of ten |
Negative powers of ten are used for small numbers:
Standard Number | Multiples of 10 | Scientific Notation | Description |
|---|---|---|---|
0.1 | 1/10 | Negative power of ten | |
0.01 | 1/10 × 1/10 | Negative power of ten | |
0.001 | 1/10 × 1/10 × 1/10 | Negative power of ten | |
0.0001 | 1/10 × 1/10 × 1/10 × 1/10 | Negative power of ten |
Practice Problems
Convert the following numbers to scientific notation:
3500:
0.0000016:
0.00730:
978 × 105:
Using Scientific Notation with Calculators
Most scientific calculators allow entry of numbers in scientific notation using the EXP or EE key. The display typically shows a number between 1 and 10 followed by 'E' and the power of ten.
Example: Entering would display as 2.4E3.
Summary
Scientific notation is essential in chemistry for expressing measurements and quantities that are very large or very small. Mastery of this notation allows for easier calculations and clearer communication of scientific data.
