Powers of Ten
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 30 of 64.
With base 10, every exponent is easy to see. A positive exponent counts the zeros: 10^2 = 100, 10^3 = 1000, and 10^6 is a million. Each step up multiplies by 10 and adds one zero.
A negative power of ten is a reciprocal: 10^-1 = 1/10 = 0.1, 10^-2 = 1/100 = 0.01, and 10^-3 = 1/1000 = 0.001. Each step down in the exponent divides the value by 10.
Powers of ten are the base of scientific notation, which the next chapter covers. In scientific notation, a number is written as a number times a power of ten.
Challenge
EasyRewrite 10^-4 as a fraction, then work out its value.
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 Power2The 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