# Scientific Notation

# 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.