Scientific notation

Learning Objectives Convert any number between standard form and scientific notation. Multiply and divide numbers expressed in scientific notation. Add and subtract numbers expressed in scientific notation by adjusting exponents. Compare and order numbers written in scientific notation. Apply the rules of scientific notation to solve real-world problems. Interpret the order of magnitude as a way to estimate and understand the scale of numbers. How many atoms are in your body, and how far away is the nearest star? ⚛️ Scientific notation is the tool mathematicians and scientists use to answer questions about the incredibly large and the infinitesimally small! This tutorial will review the fundamentals of scientific notation, a powerful method for writing and working with very...

TermDefinitionExample Scientific NotationA way of expressing numbers that are too large or too small to be conveniently written in standard decimal form. It is written as the product of a coefficient and a power of 10.The number 5,972,000,000,000,000,000,000,000 kg (the mass of the Earth) is written as 5.972 × 10^24 kg. CoefficientThe first part of a number in scientific notation. It must be a number greater than or equal to 1 and less than 10 (1 ≤ |a| < 10).In 5.972 × 10^24, the coefficient is 5.972. BaseIn scientific notation, the base is always 10.In 5.972 × 10^24, the base is 10. ExponentThe power to which the base 10 is raised. A positive exponent indicates a large number, while a negative exponent indicates a small number (a decimal between -1 and 1).In 5.972 × 10^24, the exponen...

Multiplication Rule (a × 10^n) * (b × 10^m) = (a * b) × 10^(n+m) To multiply numbers in scientific notation, multiply the coefficients and add the exponents. You may need to adjust the final result to ensure the new coefficient is between 1 and 10. Division Rule (a × 10^n) / (b × 10^m) = (a / b) × 10^(n-m) To divide numbers in scientific notation, divide the coefficients and subtract the exponents. Adjust the final result if necessary. Addition and Subtraction Rule (a × 10^n) + (b × 10^n) = (a + b) × 10^n To add or subtract, the exponents MUST be the same. If they are not, you must first adjust one of the numbers so the exponents match. Then, add or subtract the coefficients and keep the common exponent.