Multiplying and Dividing by Powers of 10

Vocabulary practice flashcards covering multiplying and dividing whole numbers and decimals by positive and negative powers of 10.

Power of 10

A mathematical expression consisting of the base $10$ raised to an exponent or index, representing repeated multiplication or division by ten.

Base

The number that is being multiplied by itself when raised to an exponent; in the context of powers of ten, the base is $10$.

Exponent / index

The superscript number that indicates how many times the base is multiplied by itself, which can be a positive, negative, or zero integer.

Decimal point

The symbol separating the whole number part from the fractional part of a decimal number, which shifts place values when multiplying or dividing by powers of ten.

Effect of multiplying by 10 on the decimal point

Shifts the decimal point one place to the right, increasing the place value of the digits.

Effect of dividing by 10 on the decimal point

Shifts the decimal point one place to the left, decreasing the place value of the digits.

Value of $10^3$

Equal to $1000$, representing ten multiplied by itself three times.

Value of $10^4$

Equal to $10000$, representing ten multiplied by itself four times.

Value of $10^{-2}$

Equal to the fraction $\frac{1}{100}$ or the decimal $0.01$.

Value of $10^{-3}$

Equal to the fraction $\frac{1}{1000}$ or the decimal $0.001$.

Value of $10^0$

Equal to $1$, representing ten raised to the power of zero.

Dividing by a positive number less than 1

A mathematical operation where dividing a positive number by a value less than $1$ (such as $10^{-3} = 0.001$) results in a larger number rather than a smaller one.

Equivalence of multiplying by $10^3$ and dividing by $10^{-3}$

The mathematical rule where multiplying a number by $1000$ yields the same result as dividing that number by $0.001$.

Kilometre to metre conversion factor

The metric conversion standard where $1\text{ kilometre} = 10^3\text{ metres}$ ($1000\text{ metres}$).