Standard Form

• Standard form, also known as scientific notation, is a way of representing very large or very small numbers to make them easier to write, read, and work with.
• A standard form number is written as A × 10^n, where A is a number between 1 and 10 (including 1 but not 10) and n is an integer.
• If the number is larger than 1, then n is positive, and denotes how many times the number must be multiplied by 10. For example, 300 can be written as 3 × 10^2.
• If the number is less than 1, then n is negative, and denotes how many times the number must be divided by 10. For example, 0.03 can be written as 3 × 10^-2.
• When converting from standard form to ordinary numbers, a positive n means to move the decimal point n places to the right, while a negative n means to move it to the left.
• When performing calculations with numbers in standard form, you may need to use laws of indices and adjust values accordingly to ensure that A remains between 1 and 10.
• You can use standard form in a calculator to perform calculations more easily. Most modern scientific calculators have a button or function to convert numbers to and from standard form.
• Applications of standard form are widespread in scientific, engineering, and mathematical fields. For instance, it’s frequently used to express distances in astronomy, sizes of atoms in physics, or probabilities in statistics.