Multiply numbers written in scientific notation

Learning Objectives Identify the coefficient and the power of 10 in a number written in scientific notation. Apply the Product Rule of Exponents to multiply powers of 10. Multiply the coefficients (decimal parts) of two numbers in scientific notation. Combine the results of multiplying coefficients and adding exponents into a single expression. Convert a final product into proper scientific notation by adjusting the coefficient and the exponent. Solve multi-step problems involving the multiplication of numbers in scientific notation. Ever wondered how astronomers calculate the mass of a galaxy containing billions of stars? 🔭 They use a powerful math shortcut to handle gigantic numbers! This tutorial will teach you how to multiply very large or very small numbers efficientl...

TermDefinitionExample Scientific NotationA way of writing very large or very small numbers as a product of a decimal number (the coefficient) and a power of 10.The number 5,800,000 is written as 5.8 \times 10^6 in scientific notation. CoefficientThe decimal part of a number in scientific notation. In proper scientific notation, its absolute value must be greater than or equal to 1 and less than 10 (1 ≤ |a| < 10).In 5.8 \times 10^6, the coefficient is 5.8. BaseIn the context of scientific notation, the base is always 10.In 5.8 \times 10^6, the base is 10. ExponentThe power to which the base (10) is raised. It indicates how many places the decimal point was moved.In 5.8 \times 10^6, the exponent is 6. Product Rule of ExponentsWhen multiplying two powers with the same base, you keep the b...

Multiplication Rule for Scientific Notation (a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n} To multiply numbers in scientific notation, multiply their coefficients and add their exponents. This is the fundamental rule for this entire topic. Adjusting to Proper Scientific Notation If (a \times b) ≥ 10, move the decimal to the left and increase the exponent. If |a \times b| < 1, move the decimal to the right and decrease the exponent. After multiplying, the new coefficient might not be between 1 and 10. You must adjust it and the exponent to put the number back into proper scientific notation.