Powers of Ten
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 30 of 64.
Base 10 makes every exponent visible. Positive exponents count zeros: 10^2 = 100, 10^3 = 1000, 10^6 is a million. Each step up multiplies by ten and appends a zero.
Negative exponents run the same staircase downward: 10^-1 = 1/10 = 0.1, 10^-2 = 1/100, three steps down is one thousandth. The exponent counts how many places the 1 sits from the decimal point: to its left for positive exponents (100), to its right for negative ones (0.01).
These powers are about to become the skeleton of scientific notation, where every measurement in science hangs a number on a power of ten.
Challenge
EasyRewrite 10^-4 as a fraction and work it out, typing each line.
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