Working with Scientific Notation

Introduction

Scientific notation is a way to express very large or very small numbers in a compact form. It is commonly used in science, engineering, and mathematics to simplify calculations and clearly show the scale of a value.

What is Scientific Notation?

A number in scientific notation is written as a × 10ⁿ, where a is a number between 1 and 10, and n is an integer (positive or negative).

• Large number example: 5,600,000 = 5.6 × 10⁶
• Small number example: 0.00042 = 4.2 × 10^-4

How to Convert Decimal to Scientific Notation

1. Move the decimal point so that only one non-zero digit remains on the left.
2. Count the number of places the decimal was moved. This is the exponent n.
3. If you moved the decimal to the left, n is positive. If to the right, n is negative.

Example: 0.00057 → 5.7 × 10^-4 (moved 4 places right)

How to Convert Scientific Notation to Decimal

1. Multiply the coefficient a by 10 raised to the exponent n.
2. Move the decimal point n places (right if positive, left if negative).

Example: 3.2 × 10³ = 3,200

Practice Examples

• Convert 0.00081 to scientific notation: 8.1 × 10^-4
• Convert 7,500,000 to scientific notation: 7.5 × 10⁶
• Convert 2.9 × 10^-2 to decimal: 0.029

Tips

• Scientific notation makes calculations with very large or small numbers easier and less error-prone.
• Always check the exponent sign: negative for small numbers, positive for large numbers.
• Use a calculator or online tool for quick conversions.

FAQ

• Why use scientific notation? It simplifies working with extremely large or small numbers and reduces mistakes in calculations.
• Can scientific notation be used in everyday life? Yes, especially in science, engineering, and when dealing with measurements like distances in space or microscopic sizes.