Divide by powers of ten

Learning Objectives Relate division by powers of ten to multiplication by negative powers of ten. Evaluate exponential functions of the form f(x) = a * 10⁻ˣ for positive integer values of x. Describe the effect of dividing a function's output by a power of ten as a vertical compression (shrink). Solve problems involving scientific notation by dividing by powers of ten. Interpret the parameters in an exponential decay model involving powers of ten. Fluently move the decimal point to divide whole numbers and decimals by powers of ten (10, 100, 1000, etc.). Ever wonder how scientists handle incredibly tiny numbers, like the mass of an atom? ⚛️ It all comes down to mastering division by powers of ten! This tutorial connects the simple act of dividing by 10, 100, or 1000 to...

TermDefinitionExample Power of TenA number that can be written in the form 10ⁿ, where n is an integer. Powers of ten are the foundation of our base-10 number system.1,000 is a power of ten because it can be written as 10³. Negative ExponentAn exponent that is a negative number. It signifies a reciprocal or division. A base raised to a negative exponent is equal to 1 divided by the base raised to the positive exponent.10⁻² is equivalent to 1 / 10² or 1/100. Scientific NotationA way of writing very large or very small numbers as a product of a number between 1 and 10 and a power of ten.The number 0.0058 is written as 5.8 x 10⁻³ in scientific notation. Exponential DecayA decrease in a quantity according to an exponential function. Repeatedly dividing by a number greater than 1 is a form of e...

Division as Negative Exponents a / 10^n = a * 10^{-n} Use this rule to convert a division problem into a multiplication problem. This is the key link between dividing by powers of ten and exponential functions. Decimal Point Shift To calculate x / 10^n This is the procedural rule for quick calculations. To divide a number by 10ⁿ, move the decimal point 'n' places to the left. Add leading zeros if necessary. Quotient Rule for Exponents 10^m / 10^n = 10^{m-n} When dividing two powers with the same base (in this case, 10), subtract the exponent of the denominator from the exponent of the numerator. This is essential for simplifying expressions in scientific notation.