Period
ArithmeticIn place value, a period is a group of three digits separated by commas, such as the ones period, thousands period, and millions period.
Definition
In large numbers, a period is a group of three digits separated by commas. Each group has its own name: ones, thousands, millions, billions, and so on.
Example
In $4{,}752{,}391$: the ones period is $391$, the thousands period is $752$, and the millions period is $4$. We read it as "four million, seven hundred fifty-two thousand, three hundred ninety-one."
Key Insight
Commas mark the boundaries between periods and make large numbers much easier to read at a glance.
Definition
A period in the place-value system is a set of three consecutive digit positions, grouped right to left. Each period (ones, thousands, millions, billions, trillions, $\ldots$) represents a $1{,}000$-fold increase over the previous. Reading numbers by period simplifies naming large numerals.
Example
$2{,}047{,}000{,}816$ has four periods: $2$ (billions), $047$ (millions), $000$ (thousands), $816$ (ones). It reads: "two billion, forty-seven million, eight hundred sixteen."
Key Insight
Each period advances by a factor of $1{,}000$ ($10^3$), which is why every period name suffix corresponds to a power of $1{,}000$: thousands $= 10^3$, millions $= 10^6$, billions $= 10^9$.
Definition
Periods correspond to groupings of three base-$10$ digits, reflecting the fact that $1{,}000 = 10^3$ is the multiplier between period names. In scientific and engineering notation, this grouping aligns with SI prefixes (kilo $= 10^3$, mega $= 10^6$, giga $= 10^9$), making the period structure consistent with international measurement conventions.
Example
The short scale (US/UK modern): $10^3 =$ thousand, $10^6 =$ million, $10^9 =$ billion. The long scale (older European): $10^6 =$ million, $10^9 =$ milliard, $10^{12} =$ billion. The period structure is the same; the naming convention differs.
Key Insight
The choice of period size three (not four or two) is historically linked to the adoption of Hindu-Arabic numerals in Europe, where grouping by thousands was a natural fit for the existing vocabulary of large number names.