Scientific notation

Learning Objectives Define scientific notation and explain its purpose. Identify numbers correctly written in scientific notation. Convert very large numbers (greater than or equal to 10) into scientific notation. Convert very small numbers (between 0 and 1) into scientific notation. Convert numbers from scientific notation back to standard form. Determine the correct sign and value of the exponent when converting numbers. Have you ever wondered how scientists talk about the distance to the sun or the size of an atom without writing endless zeros? 🤯 In this lesson, you'll learn a powerful way to write very large and very small numbers using scientific notation. This skill is essential for understanding measurements in science, technology, and everyday life, making com...

TermDefinitionExample Scientific NotationA special way to write very large or very small numbers using powers of 10, making them easier to read and work with.$6.02 imes 10^{23}$ (a very large number) or $1.6 imes 10^{-19}$ (a very small number) Standard FormThe usual way we write numbers, with all the digits and zeros shown.150,000,000 (standard form for $1.5 imes 10^8$) Coefficient (or Mantissa)The first part of a number in scientific notation. It must be a number greater than or equal to 1 and less than 10.In $3.45 imes 10^6$, the coefficient is 3.45. Power of 10The second part of a number in scientific notation, written as $10$ raised to an exponent.In $3.45 imes 10^6$, the power of 10 is $10^6$. ExponentThe small number written above and to the right of the base (in this case, 10...

General Form of Scientific Notation $a \times 10^n$ This is the structure for writing any number in scientific notation. 'a' is the coefficient, and 'n' is the exponent. Coefficient Rule $1 \le |a| < 10$ The absolute value of the coefficient 'a' must be greater than or equal to 1 and less than 10. This means there is only one non-zero digit before the decimal point. Exponent Rule for Large Numbers If the original number is $\ge 10$, then $n$ is a positive integer. When converting a large number to scientific notation, count how many places you move the decimal point to the left to get 'a'. This count is your positive exponent 'n'. Exponent Rule for Small Numbers If the original number is between $0$ and $1$,...