Back to Standard Form
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 33 of 64.
To read a number in scientific notation, move the decimal point the other way. 4.5 × 10^4 means 4.5 multiplied by ten, four times. Each multiplication by ten moves the decimal point one place to the right: 45, 450, 4500, 45000.
The digits stay the same and keep their order. Only the decimal point moves, and each empty place fills with a zero. After four moves to the right, 4.5 becomes 45000, which is the standard form of the number.
You can check your answer by counting digits. In standard form, the number of digits before the decimal point is one more than the exponent. In 4.5 × 10^4, the power is 10^4, so the standard form has five digits. 45000 has five digits.
Challenge
EasyWrite 2.7 × 10^4 in standard form. Each factor of ten moves the decimal point one place to the right. Write one line for each move.
Try it yourself
Simplify the expression
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 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