# Understanding Scientific Notation

• Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.
• It is written as a product of a number between 1 and 10 (the mantissa) and a power of 10.
• For example, the distance to the nearest star Proxima Centauri (approximately 4,000,000,000,000 kilometres) can be written as 4 x 10^12 km in scientific notation.

# Converting from Scientific Notation to Standard Form

• To convert a number from scientific notation to standard form, move the decimal point of mantissa to the right (for positive exponent) or to the left (for negative exponent) the number of places equal to the exponent.
• For example, the scientific notation 3.5 x 10^3 represents 3500.
• Conversely, 2.75 x 10^-2 corresponds to 0.0275 in standard form.

# Performing Calculations with Scientific Notation

• When multiplying numbers in scientific notation, multiply the mantissas and add the exponents.
• When dividing numbers in scientific notation, divide the mantissas and subtract the exponents.
• To add or subtract numbers in scientific notation, first convert them to the same power of ten.

# Practical Applications of Scientific Notation

• Scientific notation is used in science and engineering to handle the wide range of dimensions handled in these fields, from the microscopic scale to the cosmic scale.
• It also aids in making precise calculations with large and small numbers.
• Understanding and mastering the use of scientific notation will be key to success in subjects like physics, chemistry, and calculus.