Multiplying the Notation
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 36 of 64.
To multiply (2 × 10^3)(3 × 10^2), group the first parts together and the powers of ten together. The first parts give 2 × 3 = 6. The powers of ten follow the product rule, so 10^3 × 10^2 = 10^5. The result is 6 × 10^5, which is 600000.
To multiply two numbers in scientific notation, multiply the first parts and add the exponents of ten. Adding the exponents is the product rule for powers with the same base.
Sometimes the first parts multiply to 10 or more. If 4 × 5 = 20, the result 20 × 10^6 is not in scientific notation, because 20 is not less than 10. Move the decimal point one more place to the left and add 1 to the exponent: 2 × 10^7. Always check the first part at the end.
Challenge
EasyMultiply 4 × 10^2 × (2 × 10^3). Multiply the first parts and add the exponents. Write the result as a single power of ten, then write it in standard form.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power7Scientific Notation
Very Large NumbersBack to Standard FormMore Practice, Bigger NumbersVery Small NumbersMultiplying the NotationRecap: Scientific Notation2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative