Scientific Notation and Significant Figures

Scientific Notation

Scientific notation is a standardized way of writing very large or very small numbers that would otherwise be unwieldy to express in decimal form. It's particularly useful in scientific fields where measurements can range from subatomic particles to astronomical distances.

A number in scientific notation is written as:

Where:

• a is a number greater than or equal to 1 and less than 10 (1 ≤ a < 10)
• n is an integer (positive or negative)

The value of n indicates the direction and magnitude of the shift:

• If n is positive, the decimal point in the original number was moved n places to the left
• If n is negative, the decimal point in the original number was moved n places to the right

Converting to Scientific Notation

1. Move the decimal point so that there is exactly one non-zero digit to the left of the decimal point
2. Count how many places you moved the decimal point
3. If you moved it to the left, the exponent is positive
4. If you moved it to the right, the exponent is negative

Significant Figures

Significant figures (or significant digits) communicate the precision of a measurement or calculation. They include all digits that are known with certainty plus one digit that contains some uncertainty.

Rules for Identifying Significant Figures:

1. All non-zero digits are significant (e.g., 1, 2, 3, etc.)
2. Zeros between non-zero digits are significant (e.g., 102 has 3 significant figures)