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Final: Scientific Notation

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 58 of 62.

A data center moves 3⋅1043\cdot 10^{4} files an hour. Each file is about 2⋅1032\cdot 10^{3} kilobytes. The traffic per hour, in kilobytes, is the product of the two numbers.

To multiply two numbers in scientific notation, multiply the numbers in front and add the exponents of 10: 3⋅104⋅2⋅103=6⋅1073\cdot 10^{4}\cdot 2\cdot 10^{3} = 6\cdot 10^{7}. The product in standard form is 60000000 kilobytes an hour.

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Challenge

Medium

A satellite sends 5⋅1045\cdot 10^{4} packets an hour. Each packet is 6⋅1036\cdot 10^{3} bytes. Work out 5⋅104⋅6⋅1035\cdot 10^{4}\cdot 6\cdot 10^{3}, the number of bytes per hour. Write it in scientific notation first, then write the answer in standard form: an ordinary number with all its digits.

Try it yourself

5⋅104⋅6⋅1035\cdot 10^{4}\cdot 6\cdot 10^{3}

Simplify

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This 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 Powers

4Power of a Power

A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power

7Scientific Notation

Very Large NumbersBack to Standard FormMore Practice, Bigger NumbersVery Small NumbersMultiplying the NotationRecap: Scientific Notation

10Multiplying Polynomials

Monomial Times PolynomialMinding the SignsBinomial Times BinomialWith CoefficientsThe Square of a BinomialA Difference of SquaresRecap: Multiplying

2The Product Rule

Multiplying Same BasesWith CoefficientsRecap: The Product Rule

5Product and Quotient Powers

Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients

8What a Polynomial Is

Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials

11Dividing by a Monomial

Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing

3The Quotient Rule

Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule

6Zero and Negative Exponents

The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative

9Adding and Subtracting

Adding PolynomialsSubtracting PolynomialsThe Minus Reaches EverythingPerimeter as a PolynomialRecap: Add and Subtract

12Final Challenges

Final: Three Rules, One LineFinal: Scientific NotationFinal: The Big TidyFinal: Area, ModeledFinal: Area, ExpandedFinal: Divide and Conquer