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SL 1.1 - Scientific Notation in Mathematics

What is Scientific Notation?

Scientific notation is a standardized way to write very large or very small numbers. It's especially useful in science and engineering where we often deal with extreme values.

The Structure

A number in scientific notation is written as:

$a \times 10^n$

where:

• $a$ is a number between 1 and 10 (1 ≤ |a| < 10)
• $n$ is an integer (positive or negative)

Key Rules

1. The first number ($a$) must be greater than or equal to 1 and less than 10
2. The exponent ($n$) shows how many places to move the decimal point:

• Positive exponent: move right (for large numbers)
• Negative exponent: move left (for small numbers)

Worked Example

Converting 45,000 to scientific notation:

1. First, move the decimal point until we have a number between 1 and 10:

• 45,000 → 4.5
• We moved the decimal point 4 places to the left

2. Therefore, the number in scientific notation is: $4.5 \times 10^4$