Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. The form of a number in scientific notation is $m*10^{k}$, where m is a number with 1 digit in front of the decimal point and k is an integer. For example, 65000000000 is written as $6.5*10^{10}$ in scientific notation, and 0.0000000009 is $9*10^{-10}$ in scientific notation. To write a number in scientific notation, move the decimal point to be directly after the first (AKA leftmost) nonzero digit. If the decimal was moved n digits to the left, multiply the new number by $10^{n}$. If it was moved n digits to the right, multiply by $10^{-n}$.

Examples:

• 700: 700 = 700., so we move the decimal point two digits to the left. Thus, 700. = $7.00*10^{2}$ in scientific notation.
• 0.00051: We need to move the decimal place 4 digits to the right to place it directly after 5, so 0.00051 = $5.1*10^{-4}$ in scientific notation.
• $100{\sqrt {7000}}$: $100{\sqrt {7000}}$ is approximately 7745.97, so $100{\sqrt {7000}}\approx 7.746*10^{3}$.

Resources

• Exponents and Scientific Notation, OpenStax
• Scientific Notation, Texas A&M University
• Scientific Notation, Math Is Fun